Question

An electron enters the space between the plates of a charged capacitor as shown. The charge density on the plate is $\sigma$ . Electric intensity in the space between the plates is $E$. A uniform magnetic field $B$ also exists in that space perpendicular to the direction of $E$. The electron moves perpendicular to both $\overrightarrow{E} $ and $ \overrightarrow {B}$ without any change in direction.
The time taken by the electron to travel a distance $l$ in that space is _______

• A. $\frac {\epsilon_0 lB}{\sigma}$
• B. $\frac {\epsilon l}{\sigma B}$
• C. $\frac {\sigma l} {\epsilon _0B}$
• D. $\frac {\sigma B} {\epsilon _0 l}$

Answer 1

Answer: (A)

Here, magnetic force $=$ electrostatic force
$q v B =q E$
$v =\frac{E}{B}$
$=\frac{\sigma}{\varepsilon_{0} B}$
The time taken by electron to travel a distance $l$ in that space
$t=\frac{l}{v} =\frac{l}{\frac{\sigma}{\varepsilon_{0} B}}$
$=\frac{\varepsilon_{0} l B}{\sigma}$