JEE Main 2024 — 29 January, Shift 2 — Question 52

Lorentz force law: $\vec{F} = q(\vec{v} \times \vec{B})$. Given $q = 4.0 \times 10^{-6}\,\text{C}$, $\vec{v} = 4.0 \times 10^6 \hat{j}$, $\vec{B} = 2\hat{k}$. $\vec{v} \times \vec{B} = (4.0 \times 10^6)(2)(\hat{j}\times\hat{k}) = 8.0 \times 10^6 \hat{i}$. $\vec{F} = (4.0 \times 10^{-6})(8.0 \times 10^6)\hat{i} = 32\hat{i}\,\text{N}$. Hence, $x = 32$.