Question

A proton moving with a velocity of $2\times {10}^{6}m{s}^{-1}$ describes a circle of radius R in a magnetic field. The speed of an $\alpha$ - particle to describe a circle of same radius in the same magnetic field is

• A. $1\times {10}^6$m/s
• B. $2\times {10}^6$m/s
• C. $4\times {10}^6$m/s
• D. $8\times {10}^6$m/s

Answer 1

The correct option is A $1\times {10}^6$m/s

$r=\frac{mv}{qB}$

For proton

$r_p=\frac{m\times 2\times {10}^6}{eB}$

for $\alpha -$ particle

$r_{\alpha }=\frac{4m\times V}{2eB}$

$\because r_p=r_{\alpha }$

$2\times {10}^6=2V$

$V=1\times {10}^6$