Important Questions
1. For any charge configuration, equipotential surface through a point is normal to the electric field. Justify.
2. What is the amount of work done in moving a point charge Q around a circular arc of radius ‘r’ at the centre of which another point charge ‘q’ is located ?
3. Two uniformly large parallel thin plates having charge densities +σ and – σ are kept in the X-Z plane at a distance ‘d’ apart. Sketch an equipotential surface due to electric field between the plates. If a particle of mass m and charge ‘-q’ remains stationary between the plates, what is the magnitude and direction of the field?
Or
Two small identical electrical diploes AB and CD, each of dipole moment ‘p’ are kept 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?
4. An electric dipole of length 2 cm, when placed with its axis making an angle of 60° with a uniform electric field, experiences a torque of 6√3 Nm. Calculate the potential energy of the dipole, if it has a charge of ± 2 nC.
5. (i) Can two equipotential surfaces intersect each other? Give reasons.
(ii) Two charges -q and +q are located at points A (0, 0, –a) and B (0, 0, + a) respectively. How much work is done in moving a test charge from point P (97, 0, 0) to Q(–3, 0, 0)?
Sample Questions
1. (a) Define electric dipole moment. Is it a scalar or a vector? Derive the expression for the electric field of a dipole at a point on the equatorial plane of the dipole.
(b) Draw the equipotential surfaces due to an electric dipole. Locate the points where the potential due to the dipole is zero.
2. (i) Draw equipotential surfaces for a system of two identical positive point charges placed a distance ‘d’ apart.
(ii) Deduce the expression for the potential energy of a system of two point charges q1 and q2 brought from infinity to the points and respectively in the presence of external electric field .
3. A capacitor of unknown capacitance is connected across a battery of V volts. The charge stored in it is 360 μC. When potential across the capacitor is reduced by 120 V, the charge stored in it becomes 120 μC.
Calculate:
(i) The potential V and the unknown capacitance C.
(ii) What will be the charge stored in the capacitor, if the voltage applied had increased by 120 V?
4. A parallel plate capacitor of capacitance C is charged to a potential V. It is then connected to another uncharged capacitor having the same capacitance. Find out the ratio of the energy stored in the combined system to that stored initially in the single capacitor
5. Two capacitors of unknown capacitance C1and C2 are connected first in series and then in parallel across a battery of 100 V. If the energy stored in the two combinations is 0.045 J and 0.25 J respectively, determine the value of C1 and C2. Also calculate the charge on each capacitor in parallel combination.
