Question

A proton and an $\alpha$ particle enter a uniform magnetic field with same speed as shown in figure.

• A. Both the particles will follow same circular path in clockwise manner.
• B. Both the particles will stay for same time in the field.
• C. $\alpha$ particle will stay for more time in the field than proton.
• D. Radius of the path of proton is more than the radius of path of $\alpha$ - particle.

Answer 1

The correct option is C $\alpha$ particle will stay for more time in the field than proton.

Radius of the circular path followed by the particle, $r=\frac{mv}{qB}$
Ratio of radii of proton and $\alpha$ particle is
$\frac{r_p}{r_{\alpha }}=\frac{\frac{mu}{qB}}{\frac{4mu}{2qB}}=\frac{2}{4}=\frac{1}{2}$

$\frac{T_p}{T_{\alpha }}=\frac{\frac{2\pi m}{qB}}{\frac{2\pi 4m}{2qB}}=\frac{1}{2}$