Question

An electron moves straight inside a charged parallel plate capacitor of uniform surface charge density σ. The space between the plates is filled with constant magnetic field of induction. Neglect gravity, the time of straight line motion of the electron in the capacitor is

• A.
• B. $\frac { \varepsilon _ { 0 } \ell B } { \sigma }$
• C. $\frac { \sigma } { \varepsilon _ { 0 } \mathrm {~B} }$
• D. $\frac { \varepsilon _ { 0 } \mathrm {~B} } { \sigma }$

Answer 1

Answer: (B)

$\frac { \varepsilon _ { 0 } \ell B } { \sigma }$

Answer 2

The net electric field

The net force acting on the electron is zero because it moves with constant velocity.

$\left| \overrightarrow { \mathrm { F } } _ { \mathrm { e } } \right| = \left| \overrightarrow { \mathrm { F } } _ { \mathrm { m } } \right|$

$\Rightarrow$ eE = evB $\Rightarrow$ v= $\frac { E } { B } = \frac { \sigma } { \varepsilon _ { 0 } B }$

The time of motion inside the capacitor = t =