Question

Suppose that a proton traveling in vaccum with velocity $u_1$ at right angles to a uniform magnetic field experiences twice the force that an $\alpha$ particle experiences when it is traveling along the same path with velocity $u_2$.The ratio $\left(\frac{u_1}{u_2}\right)$ is

• A. $\frac{1}{2}$
• B. $1$
• C. $2$
• D. $4$

Answer 1

Answer: (D)

$4$

$F_p=q_p{u}_{1}B$
$F_{\alpha }=q_{\alpha }{u}_{2}B$
Given, $F_p=2F_{\alpha }$
$\therefore q_p{u}_{1}B=2q_{\alpha }{u}_{2}B$
$\therefore \frac{u_1}{u_2}=2\frac{q_{\alpha }}{q_p}=2\times 2=4$ since $q_{\alpha }=2q_p$