Q.1. Using Gauss’s law, prove that the electric field at a point due to a uniformly charged infinite plane sheet is independent of the distance from it.
Q.2. Derive an expression for the torque experienced by an electric dipole kept in a uniform electric field.
Q.3. Derive an expression for the electric field due to an infinitely long straight wire of linear charge density λ C/m.
Q.4. Derive the expression for the electric field of a dipole at a point on the equatorial plane of the dipole.
Q.5. 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.
Q.6. Deduce the expression for the electric field E due to a system of two charge q1 and q2 with position vectors r1 and r2 at a point ‘r’ with respect to common origin.
Q.7. Two charge –q each are fixed separated by distance 2d. A third charge q of mass m placed at the mid-point is displaced slightly by x (x << d) perpendicular to the line joining the two fixed charged as shown in Fig. Show that q will perform simple harmonic oscillation and also find its time period.
