An electron eneters the space between the plates of charged capacitor as shown. The carge density on the plate is `sigma`, electric intensity in the space between the plates is E, A unifrom magnetic field B aslo exists B also exists in the spae perpendicular to the direction of E.
The electron moves perpendicular to both E and B without any change in direction. The time taken by the electron to travel a distance l in the space is

Options

A. `(sigmal)/(e_(0)B)`
B. `(sigma B)/(e_(0)l)`
C. `(e_(0)lB)/(sigma)`
D. `(e_(0)l)/(sigmaB)`

Answer

C

Explanation

Here , magnetic force = electrostatic force
qvb = qE
` Rightarrow v = E/B = (omega)/(e_(0)B)`
The time taken by an electron to travel a distance l in that space, Then ` t = l/v = l/omega = (e_(0)IB)/omega`
` e_(0)B`