Physics - Magnetism Question with Solution | TestHub

Here, the magnetic force (Bqv) will provide the necessary centripetal force $\begin{array}{rl}& \left(\frac{{\mathrm{mv}}^2}{\mathrm{r}}\right)\\ \therefore & \mathrm{Bqv}=\frac{{\mathrm{mv}}^2}{\mathrm{r}}\\ \Rightarrow & \mathrm{Bqr}=\mathrm{mv}\end{array}$ For electron and proton, the magnetic field B, charge $q$ and radius $r$, all same. $\begin{array}{l}\therefore \mathrm{mv}=\text{ constant }\\ \text{ i.e. }{\mathrm{m}}_{\mathrm{e}}{\mathrm{v}}_{\mathrm{e}}={\mathrm{m}}_{\mathrm{p}}{\mathrm{v}}_{\mathrm{p}}\\ \begin{array}{rl}{\mathrm{v}}_{\mathrm{P}}& =\left(\frac{{\mathrm{m}}_{\mathrm{e}}}{{\mathrm{m}}_{\mathrm{p}}}\right){\mathrm{v}}_{\mathrm{e}}=\left(\frac{9\times 10^{-31}}{1.8\times 10^{-27}}\right)3\times 10^6\\ & =1.5\times 10^3\mathrm{m}/\mathrm{s}\end{array}\end{array}$