## Electric Charges and Fields  Important Questions for CBSE Class 12 Physics Coulombs Law, Electrostatic Field and Electric Dipole

1.Electric Charge Charge is the property associated with matter due to which it produces and experiences electric and magnetic effect. Benjamin Franklin introduced two types of charges namely positive charge and negative charge based on frictional electricity produced by rubbing two unlike objects like amber and wood.

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 ncharges q1, q2,  … ,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.Quantisation 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

• electrostatic unit, esu of charge or stat-coulomb (stat-C)
• electromagnetic unit, emu of charge or ab-C (ab-coulomb)

1 ab-C = 10 C, 1 C = 3 x 109 stat-C

8.Coulomb’s Law It states that the electrostatic force of interaction or repulsion acting between two stationary point charges is given by

9.Electrostatic forces (Coulombian forces) are conservative forces

10.Principle of Superposition of Electrostatic Forces This principle states that the net electric force experienced by a given charge particle q0 due to a system of charged particles is equal to the vector sum of the forces exerted on it due to all the other charged particles of the system.

11.Electrostatic Force due to Continuous Charge Distribution
The region in which charges are closely spaced is said to have continuous distribution of charge. It is of three types given as below:

12.Electric Field Intensity The electric field intensity at any point due to source charge is defined as the force experienced per unit positive test charge placed at that point without disturbing the source charge.It is expressed as
Here, q0 -> 0, i.e. the test charge q0 must be small, so that it does not produce its own electric field.
SI unit of electric field intensity (E) is N/C and it is a vector quantity.

13.Electric Field Intensity (EFI) due to a Point Charge
Electric field intensity at P is, then

The magnitude of the electric field at a point P is given by

If q > 0, i.e. positive charge, then E is directed away from source charge. On the other hand if q < 0, i.e. negative charge, then E is directed towards the source charge.

14.Electric Field due to a System of Charges
Same as the case of electrostatic force, here we will apply principle of superposition, i.e.

15.Electric Field Lines Electric field lines are a way of pictorially mapping the electric field around a configuration of charge(s). These lines start on positive charge and end on negative charge. The tangent on these lines at any point gives the direction of field at that point.

16.Electric field lines due to positive and negative charge and their combinations are shown as below

17.Electric Dipole Two point charges of same magnitude and opposite nature separated by a small distance altogether form an electric dipole

18.Electric Dipole Moment The strength of an electric dipole is measured by a vector quantity known as electric dipole moment (p) which is the product of the charge (q) and separation between the charges (2l).

Direction Its direction is from negative charge (- q) to positive charge (+ q).
SI unit Its SI unit is C-m.
NOTE The line joining the two charges-q and + q is called the dipole axis.
(i)Electric Field at any Point on the Axial Line/End-on Position of Electric Dipole

The direction of electric field at any point on axial line is along the direction of electric dipole moment.
(ii) Electric Field at any Point on Equatorial Line/Broadside on  Position/Perpendicular Bisector of Electric Dipole

(ii)The direction of electric field intensity (E) due to dipole at any point on equatorial line is parallel to dipole and opposite to the direction of dipole moment.
If  l<<r,

19.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.

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

### 1 Mark Questions

1.Why do the electrostatic field lines not form closed loop?[All India 2014, Delhi 2012]
Ans.The electrostatic field lines do not form closed loop because no electric field lines exist inside the charged body

2.Why do the electric field lines never cross each other?[All India 2014]
Ans.At the intersection point, there would be two directions of electric field which is not possible so lines of forces never cross each other

3.Why must electrostatic field at the surface of a charge every point? Give reason. [Foreign 2014, Delhi 2012]
Ans.As, electric field inside a conductor is always zero. The electric lines of forces exert lateral pressure on each other leads to explain repulsion between like charges. Thus, in order to stable spacing, the         lines are normal to the surface.

4.Two point charges gx and q2 are placed at a distance d apart as shown in the figure. The electric field intensity is zero at the point P on the line joining them as shown. Write two conclusions that you can draw from this. [Delhi2014c]

Ans.(i) The two point charges (q^ and q2) should be of opposite nature.
(ii) Magnitude of charge q1 must be greater than magnitude of charge q2.

5.Define dipole moment of an electric dipole. Is it a scalar quantity or a vector quantity?
[Foreign 2012; All India 2011]
Ans.Electric dipole moment of an electric dipole is equal to the product of its charges and the length of the electric dipole.It is denoted by p. Its unit is coulomb-metre.

It is a vector quantity and its direction is from negative charge towards positive charge

6.Draw a plot showing the variation of electric field (E) with distance r due to a point charge Q. [Delhi 2012]
Ans.The plot showing the variation of electric field and electric potential with distance r due to a point charge q is shown as below

7.A proton is placed in a uniform electric field directed along the position X-axis. In which direction will it tend to move? [Delhi 2011 c]
Ans.Proton will tend to move along the X-axis in the direction of a uniform electric field.

8. In which orientation, a dipole placed in a uniform electric field is in (i) stable (ii) unstable equilibrium?[Delhi 2011; All India 2008]
Ans.

9.Two point charges having equal charges separated by lm distance experience a force of 8 N. What will be the force experienced by them if they are held in water at the same distance? (Given, Kwater = 80).[Ail India 2010 C]
Ans.Two point charges system is taken from air to water keeping other variable (e.g., distance, magnitude of charge) unchanged. So, only factor which may affect the interacting force is dielectric constant of medium

10.A metallic shpere is placed in a uniform electric field as shown in the figure. Which path is followed by electric field lines and why?[HOTS; Foreign 2010]

Ans.Path d is followed by electric field lines. Electric field intensity inside the metallic sphere will be zero, therefore, no electric lines of force exist inside the sphere, also lines fall normally on the surface. Electric field lines are always perpendicular to the surface of the conductor.

11.Point out right or wrong for the following statement.The mutual forces between two charges do not get affected by the presence of other charges.
Ans.Right, because mutual force acting between two point charges is proportional to the product of magnitude of charges and inversely proportional to the square of the distance between them, i.e. independent of the other charges.

12.A dipole of dipole moment p is present in a uniform electric field E . Write the value of the angle between p and E for which the torque experienced by the dipole, is minimum.       [Delhi 2009 c]
Ans.Since, torque (x) on the dipole in electric field E is

13.Two small identical dipoles AB and CD, each of dipole moment p are kept at an angle of 120° as

shown in the figure. What is the resultant dipole moment of this combination? If this system is subjected to electric field (E) directed along + X-direction, what will be the magnitude and direction of the torque acting on this? [Delhi 2008]

Ans.

### 2 Marks Questions

14.An electric dipole of length 4 cm when placed with its axis making an angle of 60° with a uniform electric field, experiences a torque of  . Calculate the potential energy of the dipole if it has charge ± 8 nC.[Delhi 2014]
Ans.

15.An electric dipole of length 2 cm when placed with its axis making an angle of 60° with a  uniform of  electric field,experiences a torque of   Calculate the potential energy of the dipole if it has charge of ± 4 nC.[Delhi 2014]
Ans.Refer to ans. 14 (Ans. 8J).

16.An electric dipole of length 1cm which placed with its axis making an angle of 60° with  a   uniform electric field,experiences a torque of  Calculate the potential energy of the dipole if it has charge ± 2 nC. [Delhi 2014]
Ans.Refer to ans. 14 (Ans. -6J).

17.Two point charges q and – 2 q are kept d distance apart, find the location of the point relative to charge to q at which potential due to this system is zero.[All India 2014]
Ans.

18.An electric dipole is placed in a uniform electric field E with its dipole moment p parallel to the field. Find
(i)the work done in turning the dipole till its dipole moment points in the direction opposite to E.
(ii)the orientation of the dipole for which the torque acting on it becomes maximum.[All India 2014 C]
Ans.

19.A small metal sphere carrying a charge +0 is located at the centre of a spherical cavity in a large uncharged metallic spherical shell. Write the charges on the inner and outer surfaces of the shell. Write the expression for the electric field at the point Px. [Delhi 2014 c]

Ans.

20.(i) Point charge (+Q) is kept in the vicinity of and uncharged conducting plate. Sketch electric field lines between the charge and the plate.
(ii)Two infinitely large plane thin parallel sheets having surface charge densities  sigma1 and sigma2 (sigma1>sigma2) are shown in the figures. Write the magnitude and directions of net fields on the marked II and III. [Foreign 2014]

Ans.

In region II
The electric field due to the sheet of charge A will be from left of right (along the positive direction) and that due to the sheet of charge B will be from right to left (along the negative direction). Therefore, in region II we have

In region II
The electric fields due to both the charged sheets will be from left to right, i.e, along the positive direction. Therefore, in region III we have

21.Calculate the amount of work done in turning an electric dipole of dipole moment
from its position of unstable equilibrium to the position of stable equilibrium in a uniform electric field of intensity 103 N/C. [Foreign 2011]
Ans.

Ans.

23.Two identical metallic spherical shells A and B having charges + 40 and -10Q are kept a certain distance apart. A third identical uncharged sphere C is first placed in contact with sphere A and then with sphere B, then spheres A and B are brought in contact and then separated. Find the charge on the spheres A and B.[All India 2011 c]
Ans.When two identical conducting charged spheres are brought in contact, then redistribution of charge takes place, i.e. the charge is equally divided on both the spheres.
When C and A are placed in contact, charge of A equally divides in two spheres. Therefore, charge on each A and C = + 2Q

24.A dipole with a dipole moment of magnitude p is in stable equilibrium in an electrostatic field of magnitude E. Find the work done in rotating this dipole to its position of unstable equilibrium.       [All India 2010c]
Ans.

25.A dipole is present in an electrostatic field of magnitude 106N/C. If the work done in rotating it from its position of stable equilibrium to its position of unstable equilibrium is 2×10~23J, then find the magnitude of the dipole moment of this dipole.[All India 2010 C]
Ans.

26.Deduce the expression for the electric field E due to a system of two charges qx and q2 with position vectors i1 and r2 at a point r with respect to common origin. [Delhi 2010c]
Ans.

27.The sum of two point charges is 7 microC. They repel each other with a force of 1 N when kept 30 cm apart in free space. Calculate the value of each charge.   [Foreign 2009]
Ans.

28.Figure shows two large metal plates and P2 tightly held against each other and placed between two equal and unlike point charges perpendicular to the line joining them.
(i)What will happen to the plates when they are released?
(ii)Draw the pattern of the electric field lines for the system.[HOTS; Foreign 2009]

Ans.(i) By electrostatic induction, charge induces on the plates and opposite nature of charge appears on the surface facing each other. Therefore, they start attracting towards each other.

Field lines must be perpendicular to the plates. Also, equispaced field lines exist between two plates as electric field between, them is uniform.

29.Two charges + Q and -Q are kept at points (-x2,0) and (xt, 0) respectively, in the XY-plane. Find the magnitude and direction of the net electric field at the origin (0,0). [All India 2009 C]
Ans.

30.Two point charges 4Q and Q are separated by 1 m in air. At what point on the line joining of charges, is the electric field intensity zero? [All India 2008]
Ans.

### 3 Marks Questions

31.Two point charges + q and -2q are placed at the vertices B and C of an equilateral triangle ABC of side a as given in the figure. Obtain the expression for (i) the magnitude and (ii) the direction of the resultant electric field at the vertex A due to these two charges.

Ans.

32.Define the term electric dipole moment. Is it a scalar or vector? Deduce an expression for the electric field at a point on the equatorial plane of an electric dipole of length 2a.[All India 2013; Foreign 2009]
Ans.For electric dipole moment
Electric dipole moment of an electric dipole is equal to the product of its charges and the length of the electric dipole.It is denoted by p. Its unit is coulomb-metre.

It is a vector quantity and its direction is from negative charge towards positive charge
Consider an electric dipole AB consists of two charges +q and -q separated by a distance 2a. We have to find electric field at point P on equipotential line separated by a distance

33.Sketch the pattern of electric field lines due to
(i) a conducting sphere having negative charge on it.
(ii) an electric dipole.[All India 2011 C]
Ans.(i) Electric field lines due to a conducting sphere are shown in figure

(ii) Electric field lines due to an electric dipole are shown in figure

34.A positive point charge (+ q) is kept in the vicinity of an uncharged conduction plate. Sketch electric field lines originated from the point on to the surface Of the plate. [All India 2009; HOTS]
Ans.Equal charge of opposite nature induces in the surface of conductor nearer to the source charge

### 4 Marks Questions

35.Deduce the expression for the torque acting on a dipole of dipole moment p in the presence of a uniform electric field E.[All India 2014; Delhi 2008]
Ans.Torque on an Electric Dipole in a Uniform Electric Field Consider an electric dipole consisting of two charges – q and + q placed in a uniform external electric field of intensity The length of the electric dipole is 21.The dipole moment p makes an angle 0 with the direction of the electric field.
Two forces F and – F which are equal in magnitude and opposite in direction act on the dipole.

The net force is zero. Since, the two forces are equal in magnitude opposite in direction and act at different points, therefore, they constitute a couple.
A net torque x acts on the dipole about an axis passing through the mid-point of the dipole

36.While travelling back to his residence in the car, Dr. Pathak was caught up in a thunderstorm. It became very dark. He stopped driving the car and waited for thunderstorm to stop. Suddenly, he noticed a child walking alone on the road. He asked the boy to come inside the car till the thunderstorm stopped Dr.Pathak dropped the boy at his residence. The boy insisted that Dr. Pathak should meet his parents. The parents expressed their gratitude to Dr. Pathak for his concern for safety of the child.
Answer the following questions based on the above information
(i)Why is it safer to sit inside a car during a thunderstorm?
(ii)Which two values are displayed by Dr. Pathak in his action?
(iii)Which values are reflected in parents response to Dr. Pathak?
(iv)Give an example of similar action on your part in the past from everyday life.[Delhi 2013; VBQ]
Ans.(i)It is safer to be set inside a car during thunderstorm because the car acts like a Faraday cage. The metal in the car will shield you from any external electric fields and thus prevent the lightning from travelling within the car.
(ii) Awareness and humanity
(iii) Gratitude and obliged
(iv) I once came across to a situation where a puppy was stuck in the middle of a busy road during rain and was not able to go cross due to heavy flow, so I quickly rushed and helped him.

37.An electric dipole moment p is held in a uniform electric field E.
(i)Prove that no translation force acts on the dipole.
(ii)Hence, prove that the torque acting on the dipole is given by pE sin 0 indicating the direction along which it acts. [Foreign 2008]
Ans.(i)When dipole is placed in a  unifrom electric field, then force on +q charge due to electric field E

(ii)It is safer to be set inside a car during thunderstorm because the car acts like a Faraday cage. The metal in the car will shield you from any external electric fields and thus prevent the lightning from travelling within the car.
(a) Awareness and humanity
(b) Gratitude and obliged
(c) I once came across to a situation where a puppy was stuck in the middle of a busy road during rain and was not able to go cross due to heavy flow, so I quickly rushed and helped him.