Electrostatics HOTs Numerical

Question 1:

There is a uniform spherically symmetric surface charge density at a distance Ro from the origin. The charge distribution is initially at rest and starts expanding because of mutual repulsion. The figure that represents best the speed V(R(t)) of the distribution as a function of its instantaneous radius R(t) is

Question 2:

Let a total charge 2Q be distributed in a sphere of radius R, with the charge density given by ρ(r) = kr, where r is the distance from the centre. Two charges A and B, of −Q each, are placed on diametrically opposite points, at equal distance, a form the centre. If A and B do not experience any force, then:

Question 3:

Consider a sphere of radius R which carries a uniform charge density ρ. If a sphere of radius 2R is carved out of it, as shown, the ratio E_B/E_A of magnitude of electric field E_A and E_B, respectively, at points A and B due to the remaining portion will be?

Question 4:

A positive point charge is released from rest at a distance r0 from a positive line charge with uniform density. The speed (v) of the point charge, as a function of instantaneous distance r from line charge, is proportional to ?

Question 5:

A solid conducting sphere, having a charge Q, is surrounded by an uncharged conducting hollow spherical shell. Let the potential difference between the surface of the solid sphere and that of the outer surface of the hollow shell be V. If the shell is now given a charge of −4Q, then what will be new potential difference between the same both surfaces?

Question 6:

A simple pendulum of length L is placed between the plates of a parallel plate capacitor having electric field E, as shown in figure. Its bob has mass m and charge q. what will be time period of the pendulum.

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