Important Questions
1. In which orientation, a dipole placed in a uniform electric field is in (i) stable, (ii) unstable equilibrium?
2. Draw a graph to show the variation of E with perpendicular distance r from the line of charge.
3. 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 4√3 Nm. Calculate the potential energy of the dipole, if it has charge ± 8 nC.
4. A, B and C are partner’s sharing profit and losses in the ratio of ⅖, ⅖ and ⅕ respectively. C retires, A and B decide to share future profits and losses in the ratio 2 : 1. Calculate the gaining ratio.
4. A charge is distributed uniformly over a ring of radius ‘a’. Obtain an expression for the electric intensity E at a point on the axis of the ring. Hence show that for points at large distances from the ring, it behaves like a point charge.
5. How does the electric flux due to a point charge enclosed by a spherical Gaussian surface get affected when its radius is increased?
Sample Questions
1. Given a uniform electric field = 5 × 103 N/C find the flux of this field through a square of 10 cm on a side whose plane is parallel to the y-z plane. What would be the flux through the same square if the plane makes a 30o angle with the x-axis?
2. Given a uniform electric field = 2 × 103 N/C. Find the flux of this field through a square of side 20 cm, whose plane is parallel to the y-z plane. What would be the flux through the same square, if the plane makes an angle of 30° with the x-axis?
3. Given a uniform electric field = 4 × 103 N/C, find the flux of this field through a square of 5 cm on a side whose plane is parallel to the y-z plane. What would be the flux through the same square, if the plane makes an angle of 30°with the x-axis?
4. Using Gauss’s law to obtain the expression for the electric field due to a uniformly charged thin spherical shell of radius R at a point outside the shell. Draw a graph showing the variation of electric field with r, for r > R and r < R.
5. (a) Use Gauss’s theorem to find the electric field due to a uniformly charged infinitely large plane thin sheet.
(b) An infinitely large thin plane sheet has a uniform surface charge density +σ. Find the amount of work done in bringing a point charge q from infinity to a point, distance r, in front of the charged plane sheet.
