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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

`(esigma)/(epsilon_(0)lB)`

B

`(epsilon_(0)lB)/(sigma)`

C

`(esigma)/(epsilon_(0)B)`

D

`(epsilon_(0)B)/(esigma)`

Text Solution

Verified by Experts

The net electric field
`E=vecE_(1)+vecE_(2)`
`rArr E=(sigma)/(2epsilon_(0))+(sigma)/(2epsilon_(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.
`rArr vecF_("net")=vecF_(c )+vecF_(m)=0`
`rArr |vecF_(c )|=|vecF_(m)|`
`rArr eE=evB`
`rArr v=(E)/(B)=(sigma)/(epsilon_(0)B)`
`:. ` The time motion in side the capacitor `=t=(l)/(v)=(epsilon_(0)lB)/(sigma)`
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