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An electron moves staright inside a char...

An electron moves staright inside a charged parallel plate capacitor of unifrom surface charge dencity `sigma`. The space between the plates is filled with constant magnetic field of induction `vecB`. The time of staright line motion of the electron in the capacitor is

A

`(e sigma)/(epsilon_(0) l B)`

B

`(epsilon_(0) l B)/(sigma)`

C

`(e sigma)/(epsilon_(0)B)`

D

`(epsilon_(0) b)/(e sigma)`

Text Solution

Verified by Experts

The correct Answer is:
B
The net electric field
`E = E_(1) + E_(2)`
`implies E = (sigma)/(2 epsilon_(0)) + (sigma)/(2 epsilon_(0)) = (sigma)/(epsilon_(0))`
The net force acting on the electron is zero because it moves with constant velocity due to its motion on straight line.
`implies vec(F_(net)) = vec(F_(e)) + vec(F_(m)) = 0`
`implies vec(F_(e ))| = |vec(F_(m))|`
`implies eE = eVB` `implies V = (E )/(B) = (sigma)/(epsilon_(0)B)`
The time of motion in side the capacitor `t = (l)/(v) = (epsilon_(0) l B)/(sigma)`
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