Physics - Magnetism Question with Solution | TestHub

When a charge particle is allowed to move in a uniform magnetic field, then it describes spiral or circular path $$\begin{array}{l}\text{ Centripetal force, }\frac{{\mathrm{mv}}^2}{\mathrm{R}}=\mathrm{qvB}\therefore \\ \mathrm{v}=\left(\frac{\mathrm{qB}}{\mathrm{m}}\mathrm{R}\right)\\ \text{ Hence, }\sqrt{\frac{2\mathrm{qV}}{\mathrm{m}}}=\left(\frac{\mathrm{qB}}{\mathrm{m}}\right)\mathrm{R}\left[\because \mathrm{V}=\sqrt{\frac{2\mathrm{qV}}{\mathrm{m}}}\right]\\ \Rightarrow \mathrm{R}={\left(\frac{2\mathrm{mV}}{\mathrm{q}}\right)}^{1/2}\times \frac{1}{\mathrm{B}}\\ \text{ or, }\mathrm{m}\propto {\mathrm{R}}^2\end{array}$$ $[\because \mathrm{V},\mathrm{q}$ and $\mathrm{B}$ are constant $]$ $$\text{ or, }\frac{{\mathrm{m}}_1}{{\mathrm{m}}_2}={\left(\frac{{\mathrm{R}}_1}{{\mathrm{R}}_2}\right)}^2$$