A proton and an $\alpha$-particle are projected normally into a magnetic field. What will be the ratio of radii of the trajectories of the proton and $\alpha$-particle?

Question

Dr. Abubacker · Accepted Answer

(b) In perpendicular magnetic field
Magnetic force = centripetal force
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ qvB = \frac{mv^{2}}{r}\  \Rightarrow r = \frac{mv}{qB}$
For proton $\ q_{1} = e,\ m_{1} = m$
For $\mathbf{\alpha}$-particle $q_{2} = 2e,\ m_{2} = 4m$
$	herefore\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \frac{r_{1}}{r_{2}} = \frac{m_{1}v}{q_{1}B}\  	imes \frac{q_{2}B}{m_{2}v}$
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \frac{r_{1}}{r_{2}} = \frac{m}{e}\  	imes \frac{2e}{4m}$
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \frac{r_{1}}{r_{2}} = \frac{1}{2}$

Q. A proton and an $\alpha$-particle are projected normally into a magnetic field. What will be the ratio of radii of the trajectories of the proton and $\alpha$-particle?

Explanation

Reviewed by Dr. Abubacker

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