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$\vec { B }$_. Neglect gravity, the time of straight line motion of the electron in the capacitor is

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

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

$\Rightarrow \overrightarrow { \mathrm { F } } _ { \mathrm { net } } = \overrightarrow { \mathrm { F } } _ { \mathrm { e } } + \overrightarrow { \mathrm { F } } _ { \mathrm { m } } = 0$

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

⇒ eE = evB

∴ The time of motion inside the capacitor

Hence (2) is correct.