Question

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)`

Answer 1

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)`