JEE Main 2022 — Magnetic Effects of Current Question with Solution

The magnetic force on a moving charged particle is given by $\overrightarrow{F}=q\left(\overrightarrow{v}\times \overrightarrow{B}\right)$. Therefore, we know that the magnetic force is perpendicular to the magnetic field. Therefore, the resulting acceleration will also be perpendicular to the magnetic field. As the scalar product of two mutually perpendicular vectors is zero,

$$\begin{gathered} \Rightarrow \overrightarrow{a}·\overrightarrow{B}=0 \\ \Rightarrow \left(\mathrm{\alpha }\hat{\mathrm{i}}-4\hat{\mathrm{j}}\right)·\left(2\hat{\mathrm{i}}+3\hat{\mathrm{j}}\right)=0 \end{gathered}$$

$$\begin{gathered} \Rightarrow 2\alpha -12=0 \\ \Rightarrow \alpha =6 \end{gathered}$$