Question

An electron enters into a magnetic field of induction $1\times {10}^{-2}T$ with velocity $1\times {10}^{7}m/s$ and deflects into a circular path of radius $6\times {10}^{-3}m$. The specific charge of the electron is :

• A. $2.4\times {10}^{11}Ck{g}^{-1}$
• B. $1.67\times {10}^{11}Ck{g}^{-1}$
• C. $3.2\times {10}^{11}Ck{g}^{-1}$
• D. $0.8\times {10}^{11}Ck{g}^{-1}$

Answer 1

The correct option is B $1.67\times {10}^{11}Ck{g}^{-1}$

Let the e/m of electron be $L$
Centripetal force $=\frac{m{v}^2}{r}$ -------------------------(I)
Force provided by the magnetic field $=qBv$ ----------------------(II)
Equating (I) and (II),
$\frac{m{v}^2}{r}=Bqv$
$\frac{mv}{r}=Bq\Rightarrow \frac{v}{Br}=\frac{e}{m}$

$\Rightarrow L=\frac{v}{Br}=\frac{{10}^7}{{10}^{-2}\times 6\times {10}^{-3}}$

$\Rightarrow L=1.667\times {10}^{11}Ck{g}^{-1}$