Electrostatic Potential and Capacitance

Previous Years' CBSE Board Questions

2.2 Electrostatic Potential

(1 mark)

The physical quantity having SI unit N C^-1 m is (2020)

2.3 Potential due to a Point Charge

ISA. (1 mark)

2 A point charge +Q is placed at point O as shown in the figure. Is the potential difference <math>V_A - V_B</math> positive, negative or zero?

+Q •

(Delhi 2016, Foreign 2016)

2.4 Potential due to an Electric Dipole

(3 marks)

Derive the expression for the electric potential due to an electric dipole at a point on its axial line.

(2/3, Delhi 2017) Ap

<math>30^{\circ}</math> 1/r

2.5 Potential due to a System of Charges

SAI (2 marks)

4 Two small conducting balls A and B of radius <math>r_1</math> and r₂ have charges q₁ and q₂ respectively. They are connected by a wire. Obtain the expression for charges on A and B, in equilibrium. (2023)

1. N small conducting liquid droplets, each of radius r, are charged to a potential V each. These droplets coalesce to form a single large drop without any charge leakage. Find the potential of the large drop.

(2020) (An)

Answer the following questions based on the above :

1. Consider a uniformly charged thin conducting shell of radius R. Plot a graph showing the variation of <math>|\vec{E}|</math> with distance r from the centre, for points <math>0 \le r \le 3R</math>.
2. The figure shows the variation of potential V with - for two point charges Q1 and Q2, where V is the potential at a distance r due to a point charge. Find
3. An electric dipole of dipole moment of 6 × 10^-7 C-m is kept is a uniform electric field of 104 N/C such that the dipole moment and the electric field are parallel. Calculate the potential energy of the dipole.

OR

An electric dipole of dipole moment P is

initially kept in a uniform electric field E such

that p is perpendicular to E. Find the amount

of work done in rotating the dipole to a position

at which p becomes antiparallel to <math>\tilde{E}</math>. (2023)

1. Two point charges q and -2q are kept 'd' distance apart. Find the location of point relative to charge 'q' at which potential due to this system of charges is zero. (Al 2014C)

LA (4 marks)

The following questions are source based/case based questions. Read the case carefully and answer the questions that follow.

The electric potential V at any point (x, y, z) is given

by <math>V = 3x^2</math> where x is in metres and V in volts. The

electric field at the point (1 m, 0, 2 m) is

1. (b) 6 V m^-1 along +x-axis
2. (d) 1.5 V m^-1 along +x-axis. (Term I 2021-22) U Equipotentials at a large distance from a collection of charges whose total sum is not zero are
3. spheres
4. ellipsoids (d) paraboloids

1. Electrostatics deals with the study of forces, fields and potentials arising from static charges. Force and electric field, due to a point charge is basically determined by Coulomb's law. For symmetric charge configurations, Gauss's law, which is also based on Coulomb's law, helps us to find the electric field. A charge/ a system of charges like a dipole experience a force/torque in an electric field. Work is required to be done to provide a specific orientation to a dipole with respect to an electric field.

OR

"For any charge configuration, equipotential surface through a point is normal to the electric field." Justify. (Delhi 2014)

SA II (3 marks)

1. Draw the equipotential surfaces corresponding to a uniform electric field in the z-direction.

V4

1. Derive an expression for the electric potential at any point along the axial line of an electric dipole. (Al 2019)

Draw the equipotential surface due to an electric dipole. (1/3, Delhi 2019) 2 (1/5, Al 2019) (An

OR Depict the equipotential surfaces due to an electric dipole. (2/3, Delhi 2017)

Define an equipotential surface. Draw equipotential surfaces:

1. in the case of a single point charge and
2. in a constant electric field in Z-direction. Why the equipotential surface about a single charge are not equidistant?
3. Can electric field exist tangential to an equipotential surface? Give reason.

(AI 2016) R

1. Two closely spaced equipotential surfaces A and B with potentials V and V + <math>\delta V</math>, (where <math>\delta V</math> is the change in V), are kept <math>\delta l</math> distance apart as shown in

2.6 Equipotential Surfaces

MCQ

(b) planes

(Term I 2021-22)

VSA (1 mark)

Why are electric field lines perpendicular at a point

on an equipotential surface of a conductor?

(AI 2015C) U

Write two important characteristics of equipotential

surfaces. (2/5, 2020)

The magnitude of electric field (in N C^-1) in a region

varies with the distance r(in m) as

<math>E = 10r + 5</math> By how much does the electric potential increase in

moving from point at <math>r = 1</math> m to a point at <math>r = 10</math> m.

(2/5, 2020)

1. The electric potential as a function of distance 'x' is shown in the figure. Draw a graph of the electric field E as a function of x.
2. Is the electrostatic potential necessarily zero at a point where the electric field is zero? Give an example to support your answer.

(2/5, Al 2019) (Ap)

2.7 Potential Energy of a System of Charges

MCQ

A + 3.0 nC charge Q is initially at rest at a distance

of <math>r_1</math> = 10 cm from a + 5.0 nC charge q fixed at the

origin. The charge Q is moved away from q to a new

position at <math>r_2</math> = 15 cm. In this process work done by

the field is

1. 1.29 × 10^-5 J (b) 3.6 × 10⁵ J
2. <math>-4.5 \times 10^{-7} \text{ J}</math> (d) <math>4.5 \times 10^{-7}</math> J