Electric Charges and Fields

Consider an electric dipole comprising two charges +q and -q each with mass m, separated by a fixed distance d and initially at rest with its dipole moment pointing along i. A uniform electric field E j is turned on at time t=0 and it is turned off at t=tf, when the dipole moment makes an angle f with i. Neglecting any sources of energy loss, correct option(s) is/are:

1. The center of mass of the dipole is deflected towards j in the presence of the field.
2. If the magnitude of the final angular velocity f= 2qEmd, then f= 6.
3. If f= /3, then the change in kinetic energy of the dipole is given by 2 3 qEd.
4. For f= /4, the dipole rotates around its center of mass with a constant angular velocity after t>tf.

A small electric dipole p0, having a moment of inertia I about its center, is kept at a distance r from the center of a spherical shell of radius R. The surface charge density is uniformly distributed on the spherical shell. The dipole is initially oriented at a small angle as shown in the figure. While staying at a distance r, the dipole is free to rotate about its center. [figure] If released from rest, then which of the following statement(s) is(are) correct? [ 0 is the permittivity of free space.]

1. The dipole will undergo small oscillations at any finite value of r.
2. The dipole will undergo small oscillations at any finite value of r > R.
3. The dipole will undergo small oscillations with an angular frequency of 2 p0 0 I at r = 2R.
4. The dipole will undergo small oscillations with an angular frequency of p0100 0 I at r = 10R.