In a uniformly charged dielectric sphere, a very thin tunnel has been made along the diameter as shown in figure. A charge particle `-q` having mass m is released from rest at one end of the tunnel. For the situation described, mark the correct statement(s), (neglect gravity).

Options

A. Charge particle will perform SHM about center of the sphere as mean position.
B. Time period of the particle is `2pi sqrt(2piepsilon_0mR^3//qR)`
C. particle will perform oscillation but not SHM.
D. Speed of the particle while crossing the mean position is `sqrt (qQ//4piepsilon_0mR).`

Answer

A, B, D

Explanation

a.,b.,d.
At a center, the force experienced by the charge particle is zero, so it is a position of equilibrium. As we displace the charge so it is a position of equilibrium. As we displace the chare from the equilibrium position, electric force starts acting on it toward equilibrium position and hence equilibrium is a stable one. At a distance `x` from the center of sphere (equilibrium position), force experienced by the charge particle is `F=(qQx)/(4piepsilon_(0)R^(3))` [for `xltR`]
As `F=x`, it performs `SHM` about the center. Time period can be calculated by using `F=mw^(2)x`.