The charged particle moving in a uniform magnetic field of $(3\hat{i} + 2\hat{j})$ T has an acceleration $\left(4\hat{i} - \frac{x}{2}\hat{j}\right)$ m/s$^2$. The value of $x$ is ______.

JEE Main · 2026 · 05 Apr 2026 · Shift 1 · Magnetic Effects of Current

The charged particle moving in a uniform magnetic field of

(3 \hat{i} + 2 \hat{j})

T has an acceleration

(4 \hat{i} - \frac{x}{2} \hat{j})

m/s

^{2}

. The value of

x

is ______.

Answer: 12

Solution

The magnetic force

F = q (v \times B)

is always perpendicular to

B

, and since

F = m a

, the acceleration is perpendicular to the field as well, so

a \cdot B = 0

. Here

(4 \hat{i} - \frac{x}{2} \hat{j}) \cdot (3 \hat{i} + 2 \hat{j}) = 12 - x = 0

, which gives

x = 12

JEE Main · 2026 · 05 Apr 2026 · Shift 1 · Integer answer

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