Question

An electron enters the space between the plates of a charged parallel plate capacitor as shown in the figure. The charge density on the plate is σ. Electric intensity in the space between the plates is E. A uniform magnetic field B also exists in the space 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

• A. $\frac{\sigma L}{{ϵ}_{0}B}$
• B. $\frac{\sigma B}{{ϵ}_{0}L}$
• C. $\frac{{ϵ}_{0}LB}{\sigma }$
• D. $\frac{{ϵ}_{0}L}{\sigma B}$

Answer 1

The correct option is C

$\frac{{ϵ}_{0}LB}{\sigma }$

For no change in the velocity of electron, Magnetic force = electrostatic force or $qvB=qE$ $v=\frac{E}{B}=\frac{\sigma }{{ϵ}_{0}B}$ The time taken by electron to travel a distance L (t) $=\frac{L}{v}=\frac{L}{\frac{\sigma }{{ϵ}_0}B}=\frac{{ϵ}_{0}LB}{\sigma }$