Questions - Answers
Very Short Answer type Questions
1. Can there be electric potential at a point with zero electric intensity? Give an example.
A: Yes, inside a charged hallow spherical conductor.
2. Can there be electric intensity at a point with zero electric potential? Give an example.
A: Yes, a point on the equitorial line of an electric dipole.
3. What are meant by equipotential surfaces?
A: An equipotential surface is a surface with constant value of potential at all points on the surface.
4. Why is the electric field always at right angles to the equipotential surface? Explain.
A: If the electric field is not normal to the equipotential surface, then workdone in moving a charge from one point to the other will not be zero, which is a contradiction. Thus the field is normal to equipotential surface.
5. Three capacitances 1 µF, 2 µF, 3 µF are connected in parellel. (a) What is the ratio of charges? (b) What is the ratio of potential differences?
A: (a) q 
C 
q1 : q2 : q3 = C1 : C2 : C3
= 1 : 2 : 3
(b) V1 : V2 : V3 = 1 : 1 : 1
In parallel combination potential (V) differences = Constant.
6. Three capacitors of capacitances 1 µF, 2 µF, 3 µF are connected in series.
(a) What is the ratio of charges?
(b) What is the ratio of potential differences?
A: In series combination charge q = constant.
(i) q1 : q2 : q3 = 1 : 1 : 1
7. What happens to the capacitance of a parallel plate capacitor if the area of its plates is doubled?
i.e. when the area is doubled, the capacity is also doubled.
8. The dielectric strength of air is 3 × 106 V/m at certain pressure. A parallel plate capacitor with air in between the plates has a separation of 1 cm. Can you charge the capacitor to 3 × 106 V?
A: No, the dielectric strength of air means the maximum electric field that the medium will withstand.
Emax = 3 × 106 V/m d = 1 cm = 10−2 m
V = Ed = 3 × 106 × 10−2 = 3 × 104 V
Given V = 3 × 106
E > Emax, which is not possible.
Short Answer type Questions
1. Derive an expression for the electric potential due to a point charge.
A: Consider a point charge q at 'O'. Let us consider a point 'P' at a distance 'r' from 'O'. Let a unit positive charge is placed at a point 'Q' at a distance 'x' from 'O'. The electric field is along the direction 
. The force on unit positive charge is
The amount of workdone to move a unit positive test charge from Q to P through small distance dx against the field direction is dW = −F dx 
Total workdone in moving a unit positive test charge from infinity to point 'P' is
3. Derive an expression for the potential energy of an electric dipole placed in a uniform electric field?
A: Consider a dipole with charges q1 = +q, q2 = −q placed in a uniform electric field. The dipole experiences torque.
Let 'dW' be the small amount of workdone in rotating the dipole through dθ without any angular acceleration.
dW = 
dθ
dW = pE sin θ dθ
Total workdone to deflect from θ1 to θ2 is 
This workdone is stored as potential energy in the dipole. If the dipole is initially parallel to 
and turned through an angle 'θ', the workdone is
W = pE(cos 0° − cos θ)
W = pE(1 − cos θ)
The pE of the dipole in this displased position is
U = U0 + W = −pE + pE − pE cos θ
= − pE cosθ
4. Derive an expression for the capacitance of a parallel plate capacitor.
A: A parallel plate capacitor consists of two conducting metal plates P1, P2 each of area A. The two plates kept close to each other at a distance 'd' and parallel to each other. Let +
, − be the surface charge densities of two plates, P1, P2 respectively. The electric field in between the two plates will be
Where C0 is the capacitance without dielectric.
C is the capacitance with dielectric.
k is dielectric constant.
5. Explain the behaviour of dielectric in an external field.
A: The material which does not allow the charge carriers to pass through them are called dielectrics or insulators.
e.g.: Water, wood, air, mica etc.
All dielectrics are of two types. 1) Non - polar dielectrics
2) polar dielectrics.
Non - Polar Dielectrics: In these dieletrics positive charge centre coincides with negative charge centre in the absence of electric field. So, the net dipole moment of molecule is zero.
e.g.: O2 molecule. Such dielectric is placed in an external electric field 
0, the positive charge centre will be displaced in the direction of the field and negative charge centre will be displaced opposite to the field. Now each molecule is said to be polarized.
Polar Dielectrics: In case of polarised dielectrics, all positive charge centres and negative charge centres are separated. So, they will develop resultant dipole moment. In the absence of external electric field these dipole moments are random and resultant dipole moment is zero. When they are placed in external electric field the resultant dipole moment exists. Dipole moment per unit volume is called Polarisation.
= χ , χ = Susceptibility.
Long Answer type Questions
1. Define electric potential. Derive an expression for the electric potential due to an electric dipole and hence the electric potential at a point (i) on the axial line of electric dipole (ii) on the equitorial line of electric dipole.
A: Electric Potential: The amount of workdone by the external force in bringing a charge from infinity to a point is called electric potential.
Electric Dipole: Two equal and opposite charges (+q, −q) are separated by a distance (say 2a) is called electric dipole.
Potential due to a dipole: Consider an electric dipole with charges −q, +q are separated by a distance of 2a. Let 'P' be a point at a distance of 'r' from centre of dipole. Join qP, −qP and OP. The line OP makes an angle θ with the axis of dipole.
Potential at any point on the axial line:
At any point on the axial line V = V1 + V2
Potential at a point on the equitorial line:
At any point on the equitorial line = V1 + V2
2. Explain series and parallel combination of capacitors. Derive the formula for equivalent capacitance in each combination.
A: Capacitors in series: If a number of capacitors are connected in such a way that the charge on the plates every capacitor is same. Such combination is known as series combination.
Let C1, C2, C3 be the capacitances of three capacitors are connected in series.
Let V1, V2, V3 be the potential differences across C1, C2, C3 respectively. Then potential difference across the combination is
V = V1 + V2 + V3
Capacitors in parellel:
If a number of capacitors are connected in such a way that the P.D. between the plates of everyone of them is same, then the capacitors are said to be connected in parallel.
Let C1, C2, C3 are three capacitors connected in parallel. Potential difference across them is equal to V. Let q1, q2 and q3 be charges on plates of capacitors C1, C2, C3 respectively.
q = q1 + q2 + q3
CV = C1V + C2V + C3V
C = C1 + C2 + C3
If C1 = C2 = C3 then Cp = 3C
3. Derive an expression for the energy stored in a capacitor. What is the energy stored when the space between the plates is filled with a dielectric
a) with charging battery disconnected?
b) with charging battery connected in the circuit?
A: When a capacitor is charged, workdone in charging will be stored in the form of electrostatic potential energy. Let q be the charge on plates of capacitor and 'V' be the potential difference between plates. The workdone 'dW' in charging the capacitor with an additional charge is
dW = V dq.
a) When battery is disconnected, charge remains constant, but capacity increases.
The energy stored will be decreased by 'k' times.
b) When charging battery remain connected the potential difference acorss the capacitor remains same, but capacity and charge increases.
i.e. the energy stored will be increased by 'k' times.
