A charge particle is moving in a uniform magnetic field $(2 \hat{i}+3 \hat{j}) T$. If it has an acceleration of $(\alpha \hat{\mathrm{i}}-4 \hat{\mathrm{j}}) \mathrm{m} / \mathrm{s}^{2}$, then the value of $\alpha$ will be

JEE Main · 2022 · 26 Jul 2022 · Shift 1 · Magnetic Effects of Current

A charge particle is moving in a uniform magnetic field

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

. If it has an acceleration of

(α \hat{i} - 4 \hat{j}) m / s^{2}

, then the value of

α

will be

(A)3
(B)6✓ Correct
(C)12
(D)2

Answer: (B)

Solution

The magnetic force is

F = q (v \times B)

, which is always perpendicular to

B

.

Therefore,

a ⊥ B

, so

a \cdot B = 0

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

2 α - 12 = 0

α = 6

JEE Main · 2022 · 26 Jul 2022 · Shift 1 · Single correct option

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