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Moving Charges and Magnetism — Physics STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 SciencePhysicsMoving Charges and Magnetism3 Marks
Question
An $\alpha$-particle and a proton moving with the same speed enter the same magnetic field region at right angles to the direction of the field. Show the trajectories followed by the two particles in the region of the magnetic field. Find the ratio of the radii of the circular paths which the two particles may describe.
✓

Answer

Radius of charged particle in magnetic field.
$\text{r}=\frac{\text{mv}}{\text{qB}}$
$\text{r}\propto\frac{\text{m}}{q}$ for same $\upsilon$ and B.
$\frac{\text{r}_\text{p}}{\text{r}_\alpha}=\frac{(\text{m/q})_\text{p}}{(\text{m/q})_\alpha}$
$=\frac{(\text{m}_p/e)}{((4\text{m}_\text{p})/2\text{e})}=\frac{1}{2}$

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