Class 12- Chapter 1 : Electric Charges and Field

In Electrostatics, we are only concerned about the charge which is at rest, meaning the charge is not moving like the electric current. 

Chapter–1

ELECTRIC CHARGES AND FIELDS

ELECTRIC CHARGE

Charge is something associated with matter due to which it produces and experiences electric and magnetic effects.

There are two types of charges :

• Positive charge

• Negative charge

Positive and negative charges : Positive charge means the deficiency of electrons while negative charge means excess of electrons. In any neutral body the net charge is equal to zero

i.e., the sum of positive charges is equal to the sum of negative charges.

   

Charge is a scalar quantity and its SI unit is coulomb (C).

CONDUCTORS AND INSULATORS

The materials which allow electric charge (or electricity) to flow freely through them are called conductors. Metals are very good conductors of electricity. Silver, Copper and Aluminum are some of the best conductors of electricity. Our skin is also a conductor of electricity. Graphite is the only non-metal conductor of electricity.

All metals, alloys and graphite have 'free electrons', which can move freely throughout the conductor. These free electrons make metals, alloys and graphite good conductors of electricity.

Aqueous solutions of electrolytes are also conductors.

The materials which do not allow electric charge to flow through them are called non-conductors or insulators.

For example, most plastics, rubber, non-metals (except graphite), dry wood, wax, mica, porcelain, dry air etc., are insulators.

Insulators can be charged but do not conduct electric charge. Insulators do not have 'free electrons' that is why insulators do not conduct electricity.

Induced charge can be lesser or equal to inducing charge (but never greater) and its max. value is given by

Q' = – Q (1 – 1/k), where 'Q' is inducing charge and 'K' is the dielectric const. of the material of the uncharged body.

For metals k = ∞ ⇒ Q' = – Q.

METHODS OF CHARGING

1. By friction : By rubbing two suitable bodies, given in a box one is charged by +ve and another by –ve charge in equal amounts.

+ve : Glass rod, Fur, Dry hair, Wool

-ve : Silk, Ebonite rod, Comb, Amber

Note:- Electric charges remain confined only to the rubbed portion of a non-conductor but in case of a conductor, they spread up throughout the conductor.

2. By conduction : Charging a neutral body by touching it with a charged body is called charging by conduction.

It is important to note that when the bodies are charged by conduction, a charged and an uncharged body are brought into contact and then separated, the two bodies may or may not have equal charges.

If the two bodies are identical the charges on the two will be equal.

If the two bodies are not identical, the charges will be different.

The potential of the two bodies will always be the same.

3. By induction : Charging a body without bringing it in contact with a charged body is called charging by induction.

First rearrangement of charge takes place in metal rod B. When the rod B is connected to earth, electrons flow from earth to the rod B thus making it -vely charged

The magnitude of elementary positive or negative charge (electron) is the same and is equal to 1.6 × 10–19 C.

PROPERTIES OF ELECTRIC CHARGE

• Similar charges repel and dissimilar charges attract each other.

In rare situations you may find similar charged bodies attracting each other. Suppose a big positively charged body is placed near a small positively charged body then because of induction, opposite charge produced on the small body makes it attract the other body.

• A charged body attracts light uncharged bodies, due to polarisation of the uncharged body.

Fig : When a positively charged balloon is placed in contact with the wall, an opposite charge is induced with the wall, the balloon stick to the wall due to electrostatic attraction

• Charge is conserved i.e., the charge can neither be created nor be destroyed but it may simply be transferred from one body to the other.

Thus we may say that the total charge in the universe is constant or we may say that charges can be created or destroyed in equal and opposite pair. For example

(Pair-production process)

Positron is an antiparticle of electrons. It has the same mass as that of electrons but equal negative charge.

(Pair-annihilation process)

• Charge is unaffected by motion
  This is also called charge invariance with motion

Mathematically, (q)at rest = (q)in motion

• Quantisation of charge - A charge is an aggregate of a small unit of charges, each unit being known as a fundamental or elementary charge which is equal to e = 1.6 × 10–19 C. This principle states that charge on any body exists as an integral multiple of electronic charge. i.e. q = ne where n is an integer.

According to the concept of quantisation of charges, the charge q cannot go below e. On a macroscopic scale, this is as good as taking the limit q0 → 0.

Quantisation of electric charge is a basic (unexplained) law of nature. It is important to note that there is no analogous law of quantisation of mass.

Recent studies on high energy physics have indicated the presence of graphs with charge 2e/3, e/3. But since these cannot be isolated and are present in groups with total charge, therefore the concept of elementary charge is still valid.

COULOMB’S LAW

The force of attraction or repulsion between two point charges (q1 and q2) at finite separation (r) is directly proportional to the product of charges and inversely proportional to the square of distance between the charges and is directed along the line joining the two charges.

i.e., or

where ε is the permittivity of the medium between the charges.

If ε0 is the permittivity of free space, then relative permittivity of medium or dielectric constant (K), is given by

 

The permittivity of free space

 

and = 9 × 109 Nm2 C–2.

Also in the CGS system of units.

Coulomb’s law may also be expressed as

 

Let F0 be the force between two charges placed in vacuum then

 

Hence 

Therefore we can conclude that the force between two

charges becomes 1/K times when placed in a medium of

dielectric constant K.

The value of K for different media

DIELECTRIC

A dielectric is an insulator. It is of two types -

• Polar dielectric

• Non-polar dielectric

SIGNIFICANCE OF PERMITTIVITY CONSTANT OR DIELECTRIC CONSTANT

Permittivity constant is a measure of the inverse degree of permission of the medium for the charges to interact.

DIELECTRIC STRENGTH

The maximum value of an electric field that can be applied to the dielectric without its electric breakdown is called its dielectric strength.

DIFFERENCE BETWEEN ELECTROSTATIC FORCE AND GRAVITATIONAL FORCE

Note:- Both electric and gravitational forces follow inverse square law.

VECTOR FORM OF COULOMB’S LAW

SUPERPOSITION PRINCIPLE FOR DISCRETE CHARGE DISTRIBUTION: FORCE BETWEEN MULTIPLE CHARGES

The electric force on q1 due to a number of charges placed in air or vacuum is given by

Note:- Coulomb's law is valid if m and if charges are point charges.

FORCE FOR CONTINUOUS CHARGE DISTRIBUTION

A small element having charge dq is considered on the body. The force on the charge q1 is calculated as follows

Now the total force is calculated by integrating under proper limits.

i.e., 

where is a variable unit vector which points from each dq, towards the location of charge q1 (where dq is a small charge element)

TYPES OF CHARGE DISTRIBUTION

• Volume charge distribution : If a charge, Q is uniformly distributed through a volume V, the charge per unit volume ρ (volume charge density) is defined by

; ρ has unit coulomb/m3.

• Surface charge distribution : If a charge Q is uniformly distributed on a surface of area A, the surface charge density , is defined by the following equation

σ has unit coulomb / m2

• Linear charge distribution : If a charge q is uniformly distributed along a line of length λ, the linear charge density λ, is defined by

, λ has unit coulomb/m.

If the charge is non uniformly distributed over a volume, surface, or line we would have to express the charge densities as

where dQ is the amount of charge in a small volume, surface or length element.

In general, when there is a distribution of direct and continuous charge bodies, we should follow the following steps to find force on a charge q due to all the charges :

• Fix the origin of the coordinate system on charge q.

• Draw the forces on q due to the surrounding charges considering one charge at a time.

• Resolve the force in x and y-axis respectively and find and

• The resultant force is and the direction is given byand the direction is given by

CALCULATION OF ELECTRIC FORCE IN SOME SITUATIONS

• Force on one charge due to two other charges

Resultant force on q due to q1 and q2 are obtained by vector addition of individual forces

The direction of F is given by

• Force due to linear charge distribution

Let AB is a long (length ) thin rod with uniform distribution of total charge Q.

We calculate force of these charges i.e. Q on q which is situated at a distance from the edge of rod AB.

Let dQ is a small charge element in rod AB at a distance x from q .

The force on q due to this element will be

where μ is linear charge density i.e., μ = Q / .

so, newton

POINTS TO REMEMBER

1. When the distance between the two charges placed in vacuum or a medium is increased K-times then the force between them decreases K2-times. i.e., if F0 and F be the initial and final forces between them, then

2. When the distance between the two charges placed in vacuum or a medium is decreased K-times then the force between them increases K2-times. i.e., if Fo and F be the initial and final forces then F = K2Fo

3. When a medium of dielectric constant K is placed between the two charges then the force between them decreases by K-times. i.e., if Fo and F be the forces in vacuum and the medium respectively, then

4. When a medium of dielectric constant K between the charges is replaced by another medium of dielectric constant K' then the force decreases or increases by (K/K') times accordingly as K' is greater than K or K' is less than K.

ELECTRIC FIELD

The space around an electric charge, where it exerts a force on another charge is an electric field.

Electric force, like the gravitational force, acts between bodies that are not in contact with each other. To understand these forces, we involve the concept of the Electric  field. When a mass is present somewhere, the properties of space in the vicinity can be considered to be so altered in such a way that another mass brought to this region will experience a force there. The space where alteration is caused by a mass is called its Gravitational field and any other mass is thought of as interacting with the field and not directly with the mass responsible for it.

Similarly an electric charge produces an electric field around it so that it interacts with any other charges present there. One reason it is preferable not to think of two charges as exerting forces upon each other directly is that if one of them is changed in magnitude or position, the consequent change in the forces each experiences does not occur immediately but takes a definite time to be established. This delay cannot be understood on the basis of coulomb law but can be explained by assuming (using field concept) that changes in field travel with a finite speed. (≈ 3 × 108 m / sec).

Electric fields can be represented by field lines or lines of force.

The direction of the field at any point is taken as the direction of the force on a positive charge at the point.

Electric field intensity due to a charge q at any position () from that charge is defined as

where is the force experienced by a small positive test charge q0 due to charge q.

Its SI unit is NC–1. It is a vector quantity.

If there are more charges responsible for the field, then

where are the electric field intensities due to charges q1, q2, q3.....respectively.

ELECTRIC LINES OF FORCE

These are the imaginary lines of force and the tangent at any point on the lines of force gives the direction of the electric field at that point.

PROPERTIES OF ELECTRIC LINES OF FORCE

1. The lines of force diverge out from a positive charge and converge at a negative charge. i.e. the lines of force are always directed from higher to lower potential.

            

2. The electric lines of force contract length wise indicating unlike charges attract each other and expand laterally indicating like charges repel each other.

3. The number of lines that originate from or terminate on a charge is proportional to the magnitude of charge.

i.e.,

4. Two electric lines of force never intersect each other.

5. They begin from positive charge and end on negative charge i.e., they do not make closed loop (while magnetic field lines form closed loop).

6. Where the electric lines of force are

1. close together, the field is strong (see fig.1)

2. far apart, the field is weak (see fig.2)

7. Electric lines of force generate or terminate at charges /surfaces at right angles.

ELECTRIC FIELD FOR CONTINUOUS CHARGE DISTRIBUTION

If the charge distribution is continuous, then the electric field strength at any point may be calculated by dividing the charge into infinitesimal elements. If dq is the small element of charge within the charge distribution, then the electric field at point P at a distance r from charge element dq is

Non conducting sphere (dq is small charge element)

dq = λdl (line charge density)

= σ ds (surface charge density)

= ρdv (volume charge density)

The net field strength due to entire charge distribution is given by

where the integration extends over the entire charge distribution.

Note:- Electric field intensity due to a point charge q, at a distance (r1 + r2) where r1 is the thickness of medium of dielectric constant K1 and r2 is the thickness of medium of dielectric constant K2 as shown in fig. is given by

CALCULATION OF ELECTRIC FIELD INTENSITY FOR A DISTRIBUTION OF DIRECT AND CONTINUOUS CHARGE

1. Fix origin of the coordinate system where electric field intensity is to be found.

2. Draw the direction of electric field intensity due to the surrounding charges considering one charge at a time.

3. Resolve the electric field intensity in x and y-axis respectively and find ΣEx and ΣEy

4. The resultant intensity is and where θ is the angle between and x-axis.

5. To find the force acting on the charge placed at the origin, the formula F = qE is used.

ENERGY DENSITY

Energy in unit volume of electric field is called energy density and is given by

,

where E = electric field and εo= permittivity of vacuum

ELECTRIC FIELD DUE TO VARIOUS CHARGE DISTRIBUTION

• Electric Field due to an isolated point charge

• A circular ring of radius R with uniformly distributed charge

When x >> R,

[The charge on ring behaves as point charge]

E is max when . Also Emax

• A circular disc of radius R with uniformly distributed charge with surface charge density σ

• An infinite sheet of uniformly distributed charges with surface charge density σ

• A finite length of charge with linear charge density

and

Special case :

For Infinite length of charge,

∴ and 

• Due to a spherical shell of uniformly distributed charges with surface charge density σ

Ein = 0 (x < R)

• Due to a solid non conducting sphere of uniformly distributed charges with charge density ρ

 

 

• Due to a solid non-conducting cylinder with linear charge density λ

Eaxis = 0, 

,

,

In above cases,

 

POINTS TO REMEMBER

1. If the electric lines of force are parallel and equally spaced, the field is uniform.

2. If E0 and E be the electric field intensity at a point due to a point charge or a charge distribution in vacuum and in a medium of dielectric constant K then

E = KE0

3. If E and E' be the electric field intensity at a point in the two media having dielectric constant K and K' then

4. The electric field intensity at a point due to a ring with uniform charge distribution doesn't depend upon the radius of the ring if the distance between the point and the centre of the ring is much greater than the radius of the ring. The ring simply behaves as a point charge.

5. The electric field intensity inside a hollow sphere is zero but has a finite value at the surface and outside it (; x being the distance of the point from the centre of the sphere).

6. The electric field intensity at a point outside a hollow sphere (or spherical shell) does not depend upon the radius of the sphere. It just behaves as a point charge.

7. The electric field intensity at the centre of a non-conducting solid sphere with uniform charge distribution is zero. At other points inside it, the electric field varies directly with the distance from the centre (i.e. E ∝ x; x being the distance of the point from the centre). On the surface, it is constant but varies inversely with the square of the distance from the centre (i.e.). Note that the field doesn't depend on the radius of the sphere for a point outside it. It simply behaves as a point charge.

8. The electric field intensity at a point on the axis of a non-conducting solid cylinder is zero. It varies directly with the distance from the axis inside it (i.e. E ∝ x). On the surface, it is constant and varies inversely with the distance from the axis for a point outside it (i.e. ).

MOTION OF A CHARGED PARTICLE IN AN ELECTRIC FIELD

Let a charged particle of mass m and charge q be placed in a uniform electric field, then electric force on the charge particle is

∴ acceleration, (constant)

• The velocity of the charged particle at time t is,

v = u + at = at = (Particle initially at rest) or

• Distance travelled by particle is

• Kinetic energy gained by particle,

If a charged particle is entering the electric field in a perpendicular direction.

Let and the particle enters the field with speed u along the x-axis.

Acceleration along Y-axis,

The initial component of velocity along the y-axis is zero. Hence the deflection of the particle along y-axis after time t is ;

…… (i)

Distance covered by particle in x-axis,

x = ut …… (ii) ( acceleration ax = 0)

Eliminating t from equation (i) & (ii),

i.e. y ∝ x2.

This shows that the path of a charged particle in a perpendicular field is parabola.

If the width of the region in which the electric field exists be l then

1. the particle will leave the field at a distance from its original path in the direction of field, given by

2. The particle will leave the region in the direction of the tangent drawn to the parabola at the point of escape.

3. The velocity of the particle at the point of escape is given b
   
   

4. The direction of the particle in which it leaves the field is given by

ELECTRIC DIPOLE

Two equal and opposite charges separated by a finite distance constitute an electric dipole. If –q and +q are charges at distance 2l apart, then dipole moment,

Its SI unit is coulomb metre.

Its direction is from –q to +q. It is a vector quantity.

The torque τ on a dipole in uniform electric field as shown in figure is given by,

So τ is maximum, when dipole is ⊥ to field & minimum (=0) when dipole is parallel or antiparallel to field.

If and

Then

The work done in rotating the dipole from equilibrium through an angle dθ is given by

and from θ1 → θ2,

 

If θ1 = 0 i.e., equilibrium position, then

Work done in rotating an electric dipole in uniform electric field from θ1 to θ2 is W = pE (cosθ1 – cosθ2)

Potential energy of an electric dipole in an electric field is,

 

i.e. U = –pE cosθ

where θ is the angle betweenand .

We can also write 

ELECTRIC FIELD DUE TO AN ELECTRIC DIPOLE

• Along the axial line (or end-on position)

and are parallel

when x >> l

• Along equatorial line (or broadside on position)

when x >>l

When and are anti parallel then,

Eax = 2 Eeq

• At any point (from the dipole)

;

Electric field intensity due to a point charge varies inversely as a cube of the distance and in case of quadrupole it varies inversely as the fourth power of distance from the quadrupole.

ELECTRIC FORCE BETWEEN TWO DIPOLES

The electrostatic force between two dipoles of dipole moments p1 and p2 lying at a separation r is

when dipoles are placed coaxially

when dipoles are placed perpendicular to each other.

POINTS TO REMEMBER

1. The dipole moment of a dipole has a direction from the negative charge to the positive charge.

2. If the separation between the charges of the dipole is increased (or decreased) K-times, the dipole moment increases (or decreases) by K-times.

3. The torque experienced by a dipole placed in a uniform electric field has value always lying between zero and pE, where p is the dipole moment and E, the uniform electric field. It varies directly with the separation between the charges of the dipole.

4. The work done in rotating a dipole in a uniform electric field varies from zero (minimum) to 2pE (maximum). Also, it varies directly with the separation between the charges of the dipole.

5. The potential energy of the dipole in a uniform electric field always lies between +pE and –pE.

6. The electric field intensity at a point due to an electric dipole varies inversely with the cube of the distance of the point from its centre if the distance is much greater than the length of the dipole.

7. The electric field at a point due to a small dipole in end-on position is double of its value in broad side-on position,

i.e. EEnd-on = 2EBroad side-on

8. For a small dipole, the electric field tends from infinity at a point very close to the axis of the dipole to zero at a point at infinity.

9. The force between two dipoles increases (or decreases) by K4-times as the distance between them decreases (or increases) by K-times.

10. Time period of a dipole in uniform electric field is

where I = moment of inertia of the dipole about the axis of rotation.

ELECTRIC FLUX

Electric flux is a measure of the number of electric field lines passing through the surface. If surface is not open & encloses some net charge, then net number of lines that go through the surface is proportional to net charge within the surface.

For uniform electric field when the angle between area vector and electric field has the same value throughout the area,

For uniform electric field when the angle between the area vector and electric field is not constant throughout the area

POINTS TO REMEMBER

1. The electric flux is a scalar although it is a product of two vectors and (because it is a scalar product of the two).

2. The electric flux has values lying between –EA and +EA, where E and A are the electric field and the area of cross-section of the surface.

GAUSS'S LAW

It states that, the net electric flux through a closed surface in vacuum is equal to 1/εo times the net charge enclosed within the surface.

i.e.,

where Qin represents the net charge inside the gaussian surface S.

Closed surface of irregular shape which enclosed total charge Qin

In principle, Gauss's law can always be used to calculate the electric field of a system of charges or a continuous distribution of charge. But in practice it is useful only in a limited number of situations, where there is a high degree of symmetry such as spherical, cylindrical etc.

• The net electric flux through any closed surface depends only on the charge inside that surface. In the figures, the net flux through S is q1/εo, the net flux through S’ is (q2 +q3 )/εo and the net flux through S" is zero.

A point charge Q is located outside a closed surface S. In this case note that the number of lines entering the surface equals the number of lines leaving the surface. In other words the net flux through a closed surface is zero, if there is no charge inside.

• The net flux across surface A is zero

i.e.,

because Qin = – q + q = 0

APPLICATIONS OF GAUSS’S LAW

• To determine electric field due to a point charge

The point charge Q is at the centre of the spherical surface shown in figure.

Gaussian surface and is parallel to (direction normal to Gaussian surface) at every point on the Gaussian surface.

so,

• To determine electric field due to a cylindrically symmetric charge distribution

We calculate the electric field at a distance r from a uniform positive line charge of infinite length whose charge per unit length is λ = constant. The flux through the plane surfaces of the Gaussian cylinder is zero, since it is parallel to the plane of the end surface (is perpendicular to ). The total charge inside the Gaussian surface is λl, where λ is linear charge density and l is the length of the cylinder.

Now applying Gauss’s law and noting is parallel to everywhere on cylindrical surface, we find that

POINTS TO REMEMBER

1. The closed imaginary surfaces drawn around a charge are called Gaussian surfaces.

2. If the flux emerging out of a Gaussian surface is zero then it is not necessary that the intensity of the electric field is zero.

3. In the Gauss's law,

is the resultant electric field due to all charges lying inside or outside the Gaussian surface, but Qin is the charge lying only inside the surface.

4. The net flux of the electric field through a closed surface due to all the charges lying inside or outside the surface is equal to the flux due to the charges only enclosed by the surface.

5. The electric flux through any closed surface does not depend on the dimensions of the surface but it depends only on the net charge enclosed by the surface.

Very Short Answer Questions 

Q 1. Does the charge given to a metallic sphere depend on whether it is hollow or solid? Give reason for your answer. [CBSE Delhi 2017]

Ans. No, the charge given to a metallic sphere does not depend on whether it is hollow or solid because the charge only resides on the surface of the conductor. 

Q 2. Two insulated charged copper spheres A and B of identical size have charges qA and –3qA respectively. When they are brought in contact with each other and then separated, what are the new charges on them? [CBSE (F) 2011]

Ans. Charge on each copper sphere = qA – 3qA/2 = – qA

Q 3. What is the electric flux through a cube of 1 cm which encloses an electric dipole? [CBSE Delhi 2015]

Ans. The net electric flux will be zero. It is so because:

(i) Electric Flux is independent of the shape and size of the cube.

(ii) Net charge of the electric dipole is zero. 

Q 4. What orientation of an electric dipole in a uniform electric field corresponds to its (i)stable and (ii)unstable equilibrium? [CBSE Delhi 2010] [HOTS] 

Ans. (i) In stable equilibrium the dipole moment is parallel to the direction of the electric field (i.e., θ = 0).

(ii) In unstable equilibrium PE is maximum, so θ = π, i.e; the dipole moment is antiparallel to the electric field.

Q 5. Define electric field strength. Is it a vector or a scalar quantity? 

Ans. The electric field strength at a point in an electric field is defined as the electrostatic force acting on a unit positive charge when placed at that point and its direction is along the direction of electrostatic force. Electric field strength is a vector quantity.

Q 6. What kind of charge is produced while rubbing a glass rod and silk together?

Ans. While rubbing glass rod and silk together, they produce opposite charges. While the glass rod has a negative charge, the silk will have a positive charge.

Q 7.What is the name of the experiment that establishes the quantum nature of electric charge?

Ans. The experiment that establishes the quantum nature of electric charge is called – Millikan’s Oil Drop Experiment.

Q 8.A body can have a charge 8.0 x 10-20 C. Explain if the statement is true or false with logic.

Ans. This statement is false, a body can not have a charge 8.0 x 10-20 C, as it is less than the charges of electrons and protons, which determines the core charge of a body. Hence, the minimum charge a body can have is- 1.6 x 10-19.

Q 9.  Is Newton’s third law maintained by Coulomb's Law?

Ans. Coulomb Law maintains Newton’s Third Law of Motion. It states “the force experienced by two charges are equal in magnitude  but mutually opposite in direction”.

Q 10. Two equal balls having equal positive charge ‘q’ coulombs are suspended by two insulating strings of equal length. What would be the effect on the force when a plastic sheet is inserted between the two? [CBSE AI 2014]

Ans. The force will decrease upon inserting a plastic sheet. 

Reason: Force between two charges each ‘q’ in vacuum is 

F0=9x109. q2/r2

On inserting a plastic sheet (a dielectric K > 1) 

Then F=9x109. q2/Kr2.

  i.e., Force F=F0  /K

Part One : Electrostatics

What is Electrostatics

In your childhood, have you played the plastic chair and towel game? If you haven’t played yet, then let's try this interesting game. For this game, you require two to three people, one plastic chair and a towel. First of all, one person should sit on the chair with both feet above the ground (no body part should be in contact with the ground or any other thing except the chair) and then one person takes a towel and hits the back of the chair for 30 seconds. When someone will touch the person who is sitting on the chair, he or she will get a very mild electric shock. Now if you are wondering how can this happen, then the concepts of electrostatics will help you to understand this phenomenon. Electrostatics constitutes of two words “Electro” means electron or charge and “Static” means at rest. So in this plastic chair and towel game, due to the beating of the towel, the charges are generated and we get shocked due to these static charges. The similar phenomenon is when we comb our hair on a dry day and bring the comb close to tiny pieces of paper, we note that they are swiftly attracted by the comb.

 Electrostatics is a branch of physics that studies electric charges at rest or static electricity.

Electrostatic phenomena arise from the forces that electric charges exert on each other. There are many examples of electrostatic phenomena: The attraction of the plastic wrap to your hand after you remove it from a package. The attraction of paper to a charged scale. The apparently spontaneous explosion of grain silos. The damage of electronic components during manufacturing.

Part Two : Electric Charge

Electric charge

Electric charge is a fundamental property of matter and the foundation for electricity or in simpler words we can say that, Electric charge is the physical property of matter that causes it to experience a force when placed in an electromagnetic field.

      

Electrons are known to have a negative charge while protons have a positive charge.

What is Electric Charge

1.  Electric Charge is the property of subatomic particles that causes it to experience a force when placed in an electric and magnetic field. 
2.  Electric charges are of two types: Positive and Negative, commonly carried by charge carriers protons and electrons.

3.   Like charges repel each other and unlike charges attract each other.

       Examples of the types of charges are subatomic particles or the particles of matter:
            Protons are positively charged.
            Electrons are negatively charged.
            Neutrons have zero charge.

4. Electric charge is a scalar quantity.

5. Electric charges are additive in nature.

6. Electric charges are quantized.

7. Electric charges are conserved.

These last three properties of charge are called characteristics of Electric charge.

• Additivity of Electric Charge

            For a system containing n particles, the total charge of the system can be written as,

• Conservation of Electric Charge

              In an isolated system, Electric charge is conserved, which means the net electric charge of the                                system is constant. The algebraic sum of the fundamental charges in any isolated system remains 

              the same.

• Quantization of Electric Charge

             According to the principle of quantization of electric charge, all the free charges are integral multiples of a basic predefined unit which we denote by e. Thus, the charge possessed by a system can be given as,

               Where n is an integer (zero, a positive or a negative number) and e is the basic unit of charge, that is, the charge carried by an electron or a proton. The value of e is 1.6 × 10-19C.

       

 

Like charges repel each other and unlike charges attract each other.

Charging Or Electrification

The process of supplying the electric charge to an object or transferring the electric charge from an object is called charging.

An uncharged object can be charged in three different ways as follows:

• Charging by friction  
• Charging by conduction
• Charging by induction

Charging by Friction

When two objects are rubbed against each other, charge transfer takes place. One of the objects loses electrons while the other object gains electrons. The object that loses electrons becomes positively charged and the object that gains electrons becomes negatively charged. Both the objects get charged due to friction and this method of charging is commonly known as electrification by friction.

Charging by Conduction

The method of charging an uncharged object by bringing it close to a charged object is known as charging by conduction. The charged conductor has an unequal number of protons and electrons, hence when an uncharged conductor is brought near it, it discharges electrons to stabilize itself.

Charging by Induction

The process of charging an uncharged conductor by bringing it near a charged conductor without any physical contact is known as charging by induction.

  Electric Force  

     Electric Force is the repulsive or attractive interaction between any two charged bodies.  

    In Electrostatics, these are called Coulomb forces too. 

The basic difference between gravitational force and electric force is that the former one only attracts while the latter one attracts only if the charges are of opposite nature (positive and negative) and a repulsive force acts if the charges have same nature. 

Part Three : Coulomb's Law.

 Formula for Coulomb’s Law of electrostatics

+Q and +q charges are at r distance

Let two point charges +Q and +q are placed at a distance of separation r. Then according to Coulomb’s law, the electric force (F) acting between the charges is,

$\small {\color{Blue} F\propto Qq}$ and,

 $\small {\color{Blue}F\propto \frac{1}{r^{2}}}$

$\small {\color{Blue} F\propto \frac{Qq}{r^{2}}}$Then we get,    

$F\propto \frac{Qq}{r^2}$

or, ${\color{Blue}F=\frac{kQq}{r^{2}}}$ ………………….. (1)

Where, k is the Coulomb’s constant. It varies medium to medium.

In CGS unit, the value of k is 1 and in SI unit, k has an expression as ${\color{Blue} k=\frac{1}{4\pi \epsilon _{0}}}$ in air medium or free space which have the value of 9×109. Here, $\small {\color{Blue} \epsilon _{0}}$ is the permittivity of free space.

So, the equation for Coulomb’s law in air medium is,

         $\small {\color{Blue} F=\frac{1}{4\pi \epsilon _{0}}\frac{Qq}{r^{2}}}$ ……(2) in SI unit.

and, $\small {\color{Blue} F=\frac{Qq}{r^{2}}}$ ………………. (3) in CGS unit.

For the other medium, one should use the permittivity of that medium in place of the permittivity of free space.

Vector form of Coulomb’s Law 

In SI system, the magnitude of electrostatic force is given by the equation-(2). Now, the force is repulsive for two positive charges +Q and +q. So, the force on q will act along the outward direction from q. We denote the unit vector by ${\color{Blue} \widehat{r}}$ along the outward direction from q.

Then the vector form of Coulomb’s law is, $\small {\color{Blue} \overrightarrow{F}=\frac{1}{4\pi \epsilon _{0}}\frac{Qq}{r^{2}}\widehat{r}}$ …….. (4)

Again, the position vector is, $\small {\color{Blue} \overrightarrow{r}=r\widehat{r}}$. Then, $\small {\color{Blue} \widehat{r}=\frac{\overrightarrow{r}}{r}}$……….. (5)

Now, from equation-(4) and equation-(5) one can get, $\small {\color{Blue} \overrightarrow{F}=\frac{1}{4\pi \epsilon _{0}}\frac{Qq}{r^{3}}\overrightarrow{r}}$ ……… (6).

Equation-(6) is the another form of the vector form of Coulomb’s law.

Derivation of Coulomb’s Law from Gauss’s Law

The equation of Coulomb law can be derived from the Gauss law of electrostatics.

According to the Gauss’s law of electrostatics, the electric flux passing through a spherical surface of charge Q and radius r is, $\small {\color{Blue} \int \overrightarrow{E}.\overrightarrow{dS}=\frac{Q}{\epsilon _{0}}}$.

Then the electric field on the surface of the sphere due the Q charge is, $\small {\color{Blue} E=\frac{Q}{4\pi \epsilon _{0}r^{2}}}$.

If we place another charge q on the surface of the sphere, the electrostatic force on the charge q will be, F = qE.

Now, putting the equation of E in F = qE we get, $\small {\color{Blue} F=\frac{Qq}{4\pi \epsilon _{0}r^{2}}}$.

This is nothing but the Coulomb’s force equation. Hence, Coulomb’s Law is derived from the Gauss’s law.

Application of Coulomb law

The only application of Coulomb’s equation is to find the electric force between the static electric charges. One can find the value of electric field at any point by observing the Coulomb’s force at that point.

Limitations of Coulomb’s law

Here are some limitations of Coulomb law –

1. Coulomb’s law is applicable only for the point charges. To apply this law for a large body its total charge is assumed to be located at a single point (at Centre of charge) so that it can be treated as a point charge.
2. This law is valid for the charges at rest with respect to the observer.
3. Coulomb’s law is valid when the distance between the charges is greater than the nuclear distance or nuclear diameter (10-15m).

Coulomb’s Law 

Coulomb’s law is an experimental law that quantifies the amount of force that exists between two stationary electrically charged particles which is also conventionally known as the electrostatic force or Coulomb’s force.  

Coulomb’s law states that:

"The electrostatic force of attraction or repulsion between two point charges is directly proportional to the scalar multiplication of the two charges and inversely proportional to the square of the distance between them."

Scalar Form of Coulomb's Law

Vector Form of Coulomb's Law

The vector form of Coulomb's law gives both magnitude and direction of an electric force.

There are two cases depending on the nature of the charges interacting.

Case-1 : When charges are alike.

(Both are positive or both are negative.)

 q₁ >0, q₂ >0 or q₁ <0, q₂<0

Forces are repulsive in nature.

Case-2 : When charges are unlike.(Opposite charges)

q₁ >0, q₂ <0 or q₁ <0, q₂ >0,

Forces are attractive in nature.

 

Electric Force exerted by one point charge on another act along the line between the charges. It varies inversely as the square of the distance separating the charges and is proportional to the product of charges. 

The Relative Permittivity of a Medium

The relative permittivity of the medium εᵣ  can be given as

εr=K=F0Fm${\mathrm{\epsilon ᵣ}}_{}=K=\frac{{\mathrm{F₀/}}_{}}{}$Fₘ=𝛆/𝜺₀
Where,
F0 ${\mathrm{F₀}}_{}$: The force acting between two charges in the air (Vacuum)
Fm${\mathrm{Fₘ}}_{}$: Force acting between the same charges kept at the same distance in a medium

𝛆 =Permittivity of a medium, 𝜺₀ = Permittivity of Vacuum or free space

For vacuum (air), K=1$K=1$

For metals, K=∞$K=\mathrm{\infty }$

In this chapter, you will find a lot of similarities between electrostatics and gravitation. Just like gravitation, we have charge (electrons) in place of mass and the relation of Electric force is also similar .

Part Four : Superposition Principle For Forces

Superposition Principle and Electric Force due to a System of N Charges

Part Five : Electric Field

Electric Field

The space surrounding a charge or a system of charges in which the other charged particles experience electrical forces is called the electrostatic field or electric field.

An electric field is a property of space. The electric field at a point is the force per unit charge which would  be felt by a sufficiently small test charge at that point.

Electrostatic Field Strength

The strength of the electric field is measured by the force experienced by a unit positive charge placed at that point. The direction of the field is given by the direction of the unit positive charge if it were free to move.

Units

Electric field is represented with E and Newton per coulomb is the unit of it.

 

 

Electric field is a vector quantity. And it decreases with the increasing distance.

k=9.10⁹Nm²/C²

Superposition Principle and Electric Field Intensity

Part Six: Electric Field Lines

Electric Field Lines

An electric field line is an imaginary path along which a unit positive charge which is free to move travels.

1. The direction of the electric field is always tangent to the electric field lines or the lines of force.
2. The lines of force are directed towards an isolated negative charge and are directed away from the isolated positive charge.
3. The lines of force  start at the positive charge and end at the negative charge.
4. The number of field lines leaving a positive charge and terminating at a negative charge is proportional to the magnitude of the charge.
5. Two electric field lines  never intersect.
6. Electric field lines   never form closed loops.
7. In a uniform electric field, the electric field lines are equidistant and parallel to each other.

Part Seven : Electric Field  & Charge Distributions

Line charge distribution

Linear Charge distribution

When the electric charge of a conductor is distributed along the length of the conductor, then the distribution of charge is known as the line distribution of charge. A charged conductor that have length (like a rod, cylinder, etc.) has line charge distribution on it.

Linear charge density lambda

Linear charge density of a conductor is the amount of electric charge distributed per unit length of the conductor. It is denoted as the Greek letter lambda ($\color{Blue}\lambda$). It has other name as line charge density.

Linear charge density formula

If a conductor of length L has total charge Q on it, then the formula of line charge density of the conductor is, $\color{Blue}\lambda=\frac{Q}{L}$……..(1)

This is the most general equation of linear charge density and is applicable for any linear conductor.

Unit of line charge density

The SI unit of line charge density (lambda) is Coulomb/meter (C.m-1) and CGS unit is StatC.cm-1.

Dimensional formula of line charge density

The dimension of electric charge [TI] and that of the length is [L]. So, the dimensional formula of the line charge density is [L-1TI].

Integral relation between total charge and line charge density

Let us consider a linear conductor of length L has the line charge density $\lambda$.

The amount of charge on an elementary length dl is, $\color{Blue}dQ=\lambda.dl$

Now, total charge on the conductor is, $\color{Blue}Q=\int \lambda.dl$……….(2)

This formula of line charge density is applicable only for a continuous body.

How to find linear charge density of a cylinder?

Here, we are going to understand the thing with the help of an example. Let, a cylinder of length 15 cm has total charge of +2C on it. We want to find the line charge density of the cylinder.

So, the total charge, Q = 2C and length L = 15 cm = 0.15 m

Then, the line charge density of the cylindrical conductor is, $\color{Blue}\lambda=\frac{2}{0.15}$

or, $\color{Blue}\lambda=13.33$ C/m.

Formula for Surface charge density

If Q amount charge is distributed over the surface of a conductor of total surface area A, then the formula of surface charge density for the conductor is $\small {\color{Blue} \sigma =\frac{Q}{A}}$

Different conductors of the same charge can have different values of surface charge density. Because it depends on the area and curvature of the surface.

Units of Surface Charge density

Unit of Surface charge density = Unit of charge/unit of area

The SI unit of charge is Coulomb (C) and the SI unit of surface area is m2 .

So, the SI unit of surface charge density is C/m2 .

Similarly, one can find that the CGS unit of surface charge density is esu/cm2 .

Dimension of surface charge density

The dimension of electric charge is [TI] and the dimension of surface area is [L2].

So, the dimensional formula of Surface charge density of a conductor is [ L-2 TI ].

Volume charge distribution

In a three dimensional (3D) conductor, electric charges can be present inside its volume. This type of distribution of electric charge inside the volume of a conductor is known as the volume charge distribution. A spherical conductor, a cylindrical conductor, etc. can have volume charge distribution.

What is volume charge density?

The volume charge density of a conductor is defined as the amount of charge stored per unit volume of the conductor. Only the conductors with three dimensional (3D) shapes like a sphere, cylinder, cone, etc. can have volume charge density.

Symbol of Volume charge density

The volume density of charge is represented by the Greek letter rho ($\color{Blue}\rho$).

Volume charge density equation

If Q be the amount of charge inside a volume V of a conductor, then the formula for volume charge density of the conductor is, $\color{Blue}\rho=\frac{Q}{V}$…….(1)

This is the fundamental equation of volume density of electric charge. Since, the formula of volume is different for different shapes, the formula of volume charge density also has different forms for conductors of different shapes. These formulae are at below.

Volume charge density unit

SI unit of electric charge is Coulomb (C) and of volume is m3. Therefore, the SI unit of volume density of charge is C.m-3 and the CGS unit is StatC.cm-3.

Dimension of Volume charge density

The dimension of electric charge is [TI] and the dimension of volume is [L3]. Then, the dimensional formula of volume charge density is [L-3TI].

Volume charge density formula of different conductors

As the volume formula is different for the conductors of different shapes, therefore we can get different forms for the volume charge density formula for different shapes.

Volume charge density of sphere

Charged sphere

If a spherical conductor of radius R contains Q amount of charge inside its volume, then the formula for the volume charge density of the sphere is, $\color{Blue}\rho=\frac{Q}{\frac{4}{3}\pi R^{3}}$………(2)

Volume charge density of cylinder

If a cylindrical conductor of length L and radius r contains Q amount of charge inside its volume, then the formula of volume charge density of the cylinder is $\color{Blue}\rho=\frac{Q}{\pi r^{2} L}$……..(3)

Integral relation between charge and volume charge density

From equation-(1), electric charge = volume charge density × volume

The integral form of this relation is, $\color{Blue}Q = \int\rho .dV$……..(4)

Electric Field Due to Various Charge Distribution

A Charge distribution may be Discrete or Continuous. When a large number of point charges constitute a system, it is called a Discrete charge distribution. But in case of Continuous Charge Distribution, it has three different modes of appearances. They are :

• Linear Charge Distribution
• Surface Charge Distribution
• Volume Charge Distribution 

A Continuous Charge Distributions

Part Eight : Electric Dipole

Another important concept in this chapter is an electric dipole (forms when a pair of equal and opposite point charges are separated by a fixed distance) which occurs in nature in a variety of situations.

 The Hydrogen Fluoride molecule (HF) is a typical example of an electric dipole. Every electric dipole is characterized by its electric dipole moment which is a vector “p” directed from negative to the positive charge. 

In gravitation, we do not have dipoles can you suggest why?

Electric Dipole :
An Electric Dipole is formed when two charges of equal magnitude and opposite nature are separated by a small distance.

Electric Dipole Moment :

It is a vector  representing the product of the magnitude of either charge of the dipole and its length.

              p = q . 2l = 2ql

 

Electric Field due to a Dipole Electric field of an electric dipole is the space around the dipole in which the electric effect of the dipole can be experienced.

Derive an expression for electric field due to electric dipole along its equatorial axis at a perpendicular distance r from its centre.

In this case we have to determine the electric field at a point P  located on the perpendicular bisector of the line joining the two charges. Let the distance of P from this line be y.

                                                

Magnitude of electric field at P due to – q:

                                   

 is directed from P to A. It has vertical component directed in the -y direction, and a horizontal component directed in the – x direction.

Magnitude of E at P due to + q:

                   

 is directed from B to P. It has vertical component directed in the +y direction, and a horizontal component directed in the – x direction.

 The net electric field at P is calculated by adding vectorially  and .

As their vertical components,  and , are equal in magnitude but opposite in direction.  Hence they cancel out.

And, the horizontal components are both in the –x direction. Hence they add up.

Thus,

 

Using simple trigonometry, where we can substitute cos θ in terms of a and y, we get

                                                                                                                                                                                    

     

         

For, neglect  in the denominator.

Thus, we get

                   

But the dipole moment of an electric dipole is

                   

If we replace y in the expression by r  and a by l to match our previous question dealing with field at a point on the axial line, we shall get 

 

Torque on an electric dipole placed in a uniform electric field 

Torque on an electric dipole placed in a uniform electric field (E) is given by

𝜏 = p  × E 

•   Dipole is in stable equilibrium in uniform electric field when angle between p and E is 0° and in unstable equilibrium when angle θ= 180°.
•   Net force on electric dipole placed in a uniform electric field is zero.
•   There exists a net force and torque on electric dipole when placed in non-uniform electric field.
•   Work done in rotating the electric dipole from θ1 to θ2 is W = p E (cos θ1 – cos θ2)
•   Potential energy of electric dipole when it rotates from θ1 = 90° to θ2 =0

                             

•   Work done in rotating the dipole from the position of stable equilibrium to unstable equilibrium, i.e. when θ1 = 0° and θ2 = π.

                         W = 2 p E

•   Work done in rotating the dipole from the position of stable equilibrium to the position in which dipole experiences maximum torque, i.e. when θ1 = 0° and θ2 = 90°.

                        W = p E

Part Nine : Electric Flux and Area Vector

Electric Flux

The electric flux through a surface is defined as the number of lines of force passing normally through the surface. The flux per unit area of the surface at any point in an electric field is the measure of the electric intensity at that point.

Part Ten : Gauss Theorem and Its Applications

Gauss Theorem

The Gauss theorem states that for any charge distribution, the total electric flux linked with a closed surface is 1/ε0 times the total charge enclosed by the surface.

Mathematically,

 

Statement of Gauss’s law

Gauss’s law in electrostatics states that the electric flux passing through a closed surface is equal to the $\small \frac{1}{\epsilon _{0}}$ times total charge enclosed by the surface. Gauss’s law gives the expression for electric field for charged conductors. This law has a wide use to find the electric field at a point.

Gauss law formula

Let a closed surface is containing q amount of charge inside it. Now, according to Gauss’s law of electrostatics, total electric flux passing through the closed surface is, $\small \phi =\frac{q}{\epsilon _{0}}$ ……………(1)

Now, the electric flux through a surface S in the electric field E is, $\small \phi =\oint \vec{E}.d\vec{S}$…………..(2)

Then from equation-(1) and equation-(2) we get, $\small \oint \vec{E}.d\vec{S}=\frac{q}{\epsilon _{0}}$………….(3)

This is the equation or formula for Gauss’s law. It is the integral form of Gauss’s law equation. Using this formula one can find the electric field for symmetrically charged conductors.

Differential form of Gauss’s law

We have the integral form of Gauss’s law as, $\small \oint \vec{E}.d\vec{S}=\frac{q}{\epsilon _{0}}$

Now, if $\small \rho$ be the volume charge density then charge, $\small q=\int \rho dV$

Again, from Gauss’s divergence theorem, $\small \int \vec{E}.d\vec{S}=\int \triangledown .\vec{E} dV$

Then equation-(3) can be written as, $\small \int \triangledown .\vec{E} dV = \int \frac{\rho }{\epsilon _{0}}dV$

or, $\small \int [\triangledown .\vec{E} - \frac{\rho }{\epsilon _{0}} ]dV = 0$

or, $\small \triangledown .\vec{E} - \frac{\rho }{\epsilon _{0}} = 0$

Then, $\small \triangledown .\vec{E} = \frac{\rho }{\epsilon _{0}}$ ………………..(4)

This is the differential form of the Gauss’s law of electrostatics.

Equation of Gauss law inside a Conductor

The electric field inside a conductor is zero. Because the net electric charge inside the conductor becomes zero. Hence, no electric flux is enclosed inside the conductor. Therefore, the Gauss’s law inside a conductor can be written as, $\small \phi =\oint \vec{E}.d\vec{S}=0$

Explanations:

• Gauss’s Law: The flux of electric field through any closed surface S is 1/ε₀ times the total charge enclosed by S.
• Electric field outside the charged shell is as though the total charge is concentrated at the centre. The same result is true for a solid sphere of uniform volume charge density.

• The electric field is zero at all points inside a charged shell.

Electric field E, due to an infinitely long straight wire of uniform linear charge

• Electric field E, due to an infinitely long straight wire of uniform linear charge density  𝛌 is 

where r is the perpendicular distance of the point from the wire and is the radial unit vector in the plane normal to the wire passing through the point.

Electric field E, due to an infinite thin plane sheet of uniform surface charge density σ

 

• Electric field E, due to an infinite thin plane sheet of uniform surface charge density σ: 

       

Where       is a unit vector normal to the plane, outward on either side.

Electric field E, due to thin spherical shell of uniform surface charge density σ

• Electric field E, due to thin spherical shell of uniform surface charge density σ:

                        E=0 (r<R)

              

• where r is the distance of the point from the centre of the shell and R the radius of the shell, q is the total charge of the shell & q = 4πR²σ.

        Hence, 

Other Facts :

• Electric field E along the outward normal to the surface is zero.
•  σ is the surface charge density. 
• Charges in a conductor can reside only at its surface. 
• Potential is constant within and on the surface of a conductor. 
• In a cavity within a conductor (with no charges), the electric field is zero.

Applications of Gauss’s law

The main purpose of the Gauss’s law in electrostatics is to find the electric field for different type of conductors. This law can be used to find the electric field for a

• Point charge
• Uniformly charged infinitely long wire
• Charged spherical conductor
• Cylindrical conductor
• Infinitely charged plane
• Inside a capacitor

Also, one can find the electric flux through a closed surface by using this law. In this case, the total charge inside the surface should be known.

Extra Reading

Electrostatic phenomena arise from the forces that electric charges exert on each other. There are many examples of electrostatic phenomena: The attraction of the plastic wrap to your hand after you remove it from a package. The attraction of paper to a charged scale. The apparently spontaneous explosion of grain silos. The damage of electronic components during manufacturing.

Properties of Charges at Rest

Electrostatics is the study of charges, or charged bodies, at rest. When positive or negative charge builds up in fixed positions on objects, certain phenomena can be observed that are collectively referred to as static electricity. The charge can be built up by rubbing certain objects together, such as silk and glass or rubber and fur; the friction between the objects causes electrons to be transferred from one to the other—from a glass rod to a silk cloth or from fur to a rubber rod—with the result that the object that has lost the electrons has a positive charge and the object that has gained them has an equal negative charge. An electrically neutral object can be charged by bringing it in contact with a charged object: if the charged object is positive, the neutral object gains a positive charge when some of its electrons are attracted onto the positive object; if the charged object is negative, the neutral object gains a negative charge when some electrons are attracted onto it from the negative object.

A neutral conductor may be charged by induction using the following procedure. A charged object is placed near but not in contact with the conductor. If the object is positively charged, electrons in the conductor are drawn to the side of the conductor near the object. If the object is negatively charged, electrons are drawn to the side of the conductor away from the object. If the conductor is then connected to a reservoir of electrons, such as the ground, electrons will flow onto or off of the conductor with the result that it acquires a charge opposite to that of the charged object brought near it

Properties of Electric Charges

According to modern theory, most elementary particles of matter possess charge, either positive or negative. Two particles with like charges, both positive or both negative, repel each other, while two particles with unlike charges are attracted (see Coulomb's law). The electric force between two charged particles is much greater than the gravitational force between the particles. The negatively charged electrons in an atom are held near the nucleus because of their attraction for the positively charged protons in the nucleus.

Electric Potential

The electric potential at a point in an electric field is defined as the amount of work done in moving a unit positive charge from infinity to the point against the electric field. The SI unit of potential is Volt.

Relation between electric field and electric potential

The electric field E = – (dV/dx)

dV/dx is the rate of change of potential with distance.

 

Electrostatics is the branch of physics that studies the effects generated in bodies according to their electrical charges in equilibrium.

The electric force (F) is proportional to the charges brought together and is inversely proportional to the distance between them. This force acts between the charges radially, that is, a line between the charges; hence it is a radial vector between the two charges.

Likewise, this force depends on the electric charge and the distance between them. It is a fundamental principle of electrostatics and law applicable to charges at rest in a reference system.

It is worth mentioning that for small distances, the forces of the electric charges increase, and for considerable distances, the forces of the electric charges decrease. Hence, it is reduced as the charges move away from each other.

The coulomb (symbol: C) is the SI derived unit of electric charge.^[2] Historically, it was defined as the charge delivered by an electric current of one ampere in one second, with the ampere being defined as the current needed to generate a magnetic force of 0.2 micronewtons per metre between 2 parallel wires 1 metre apart.^[3] Under the 2019 redefinition of the SI base units, which took effect on 20 May 2019, the elementary charge was assigned the exact value of 1.602176634×10⁻¹⁹ C,^[2] making the coulomb exactly 1/(1.602176634×10⁻¹⁹) = 10¹⁹/1.602176634 elementary charges. The same number of electrons has the same magnitude but opposite sign of charge, that is, a charge of −1 C. This makes the coulomb one of the few SI units to depend on the value of only one of the SI defining constants. Despite this, the coulomb is, somewhat incongruously, still classified as a derived unit, and the ampere is still classified as an SI base unit.

Limitations of Coulomb’s Law

1. The validity of Coulomb’s Law is determined by the number of molecules of solvent between the two charged bodies. If the average number of solvent molecules between the two interacting charged particles is large enough, we can only apply this law.
2. We can only apply Coulomb’s Law on stationary charges.
3. If the shape of the charged body is arbitrary, then we will not be able to determine the distance between the charges, and it becomes difficult to apply this law.

 

Electric Charge Charge is the property associated with matter due to which it produces and experiences electric and magnetic effect.
2. Conductors and Insulators Those substances which readily allow the passage of electricity through them are called conductors, e.g. metals, the earth and those substances which offer high resistance to the passage of electricity are called insulators, e.g. plastic rod and nylon.
3. Transference of electrons is the cause of frictional electricity.
4. Additivity of Charges Charges are scalars and they add up like real numbers. It means if a system consists of n charges q1, q2, q3 , … ,qn, then total charge of the system will be q1 +q2 + … +qn.
5. Conservation of Charge The total charge of an isolated system is always conserved, i.e. initial and final charge of the system will be same.
6. Quantization of Charge Charge exists in discrete amount rather than continuous value and hence, quantised.
Mathematically, charge on an object, q=±ne
where, n is an integer and e is electronic charge. When any physical quantity exists in discrete packets rather than in continuous amount, the quantity is said to be quantised. Hence, charge is quantised.
7. Units of Charge
(i) SI unit coulomb (C)
(ii) CGS system
(a) electrostatic unit, esu of charge or stat-coulomb (stat-C)
(b) electromagnetic unit, emu of charge or ab-C (ab-coulomb)
1 ab-C = 10 C, 1 C = 3 x 109 stat-C

Thanks for reading .See you in the next Chapter.

Bye.

Subhas C Chakra

@www.studylearnexploreccc.com