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I a uniformly positively charged sphere ...

I a uniformly positively charged sphere a very thin tunnel has been made along the diameter as shown in the figure below. A carged particle -`q` having mass m is released from rest at one end of tunnel. For the situation described, mark out the correct statement (s) : [Neglect gravity]

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).`

Text Solution

Verified by Experts

The correct Answer is:
A, B, D
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`.
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