Physics - Magnetism Question with Solution | TestHub

Here, $\vec{v}=3\hat{i}+2\hat{j}\mathrm{m}{\mathrm{s}}^{-1}$ $\vec{B}=2\hat{j}+3\hat{k}\mathrm{T}$ Specific charge of proton $=\frac{e}{m}=0.96\times 10^8\mathrm{C}{\mathrm{kg}}^{-1}$ Force on a proton in a uniform magnetic field is $\begin{array}{rl}& \vec{F}=e(\vec{v}\times \vec{B})\\ & =e[(3\hat{i}+2\hat{j})\times (2\hat{j}+3\hat{k})]\\ & =e(6\hat{k}-9\hat{j}+6\hat{i})=e(6\hat{i}-9\hat{j}+6\hat{k})\mathrm{N}\end{array}$ Acceleration of the proton, $\begin{array}{rl}& \vec{a}=\frac{\vec{F}}{m}=\frac{e(6\hat{i}-9\hat{j}+6\hat{k})}{m}\\ & =0.96\times 10^8(6\hat{i}-9\hat{j}+6\hat{k})\mathrm{m}{\mathrm{s}}^{-2}\\ & =2.88\times 10^8(2\hat{i}-3\hat{j}+2\hat{k})\mathrm{m}{\mathrm{s}}^{-2}\end{array}$