Question

A small electric dipole \(\bar{P_0}\), 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 \(\sigma\)is uniformly distributed on the spherical shell. The dipole is initially oriented at a small angle 𝜃 as shown in the figure. While staying at a distance r, the dipole is free to rotate about its center.If released from rest, then which of the following statement(s) is(are) correct?

If released from rest, then which of the following statement(s) is(are) correct?

• A. The dipole will undergo small oscillations at any finite value of r > R.
• B. The dipole will undergo small oscillations at any finite value of r > R.
• C. The dipole will undergo small oscillations with an angular frequency of \(\sqrt\frac{2\sigma p_0}{\epsilon_0I} \ at\ r=2R\)
• D. The dipole will undergo small oscillations with an angular frequency of \(\sqrt\frac{6 p_0}{100\epsilon_0I} \ at\ r=10R\)

Answer 1

The Correct Option is B, D

The correct option is (B): The dipole will undergo small oscillations at any finite value of r > R. and (D): The dipole will undergo small oscillations with an angular frequency of \(\sqrt\frac{6 p_0}{100\epsilon_0I} \ at\ r=10R\)