A small electric dipole 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 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? [𝜀0 is the permittivity of free space.] (A) The dipole will undergo small oscillations at any finite value of 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 √ 2𝜎𝑝0 𝜖0𝐼 at r = 2𝑅. (D) The dipole will undergo small oscillations with an angular frequency of √ 𝜎𝑝0 100𝜖0𝐼 at r = 10R.
A small electric dipole 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 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? [𝜀0 is the permittivity of free space.] (A) The dipole will undergo small oscillations at any finite value of 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 √ 2𝜎𝑝0 𝜖0𝐼 at r = 2𝑅. (D) The dipole will undergo small oscillations with an angular frequency of √ 𝜎𝑝0 100𝜖0𝐼 at r = 10R.