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A cavity of radius r is made inside a ...

A cavity of radius r is made inside a solid sphere. The volume charge density of the remaining sphere is `rho`. An electron (charge e, mass m) is released inside the cavity from point P as shown in figure. The centre of sphere and center of cavity are separated by a distance a. The time after which the electron again touches the sphere is

A

`sqrt((6sqrt(2)repsilon_0m)/(epa))`

B

`sqrt((sqrt(2)repsilon_0m)/(epa))`

C

`sqrt((6repsilon_0m)/(epa))`

D

`sqrt((repsilon_0m)/(epa))`

Text Solution

Verified by Experts

The correct Answer is:
A
a. Acceleration of electron
`A=eE//m` (in backward direction).

and `E=(pa)/(3epsilon_(0))` or `A=(epa)/(2epsilonm)`
Distance traveled by electron where it hits the wall of cavity is `S=2rcostheta=(r)/(sqrt(s)`
Hence using `s=(1)/(2)At^(2)`
`t=sqrt((6sqrt(2)repsilon_(0)m)/(epa))`
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