In a certain region static electric and magnetic fields exist. The magnetic field is given by B = B₀(i + 2j - 4k). If a test charge moving with a velocity v = v₀(3i - j + 2k) experiences no force in that region, then the electric field in the region, in SI units, is: (a) E = -v₀B₀(3i - 2j - 4k) (b) E = -v₀B₀(i + j + 7k) (c) E = v₀B₀(14j + 7k) (d) E = -v₀B₀(14j + 7k)

Answer: (d). No force: qE + qv × B = 0 ⇒ E = -v × B. (3i - j + 2k) × (i + 2j - 4k) = (4 - 4)i + (2 + 12)j + (6 + 1)k = 14j + 7k E = -v₀B₀(14j + 7k) So the answer is (d).

In a certain region static electric and magnetic fields exist. The… | JEE Main 2017 (8 Apr, Shift 1)

Q96JEE Main 2017 · 8 APR · SHIFT 1Medium

Moving Charge in a Magnetic Field

In a certain region static electric and magnetic fields exist. The magnetic field is given by $\vec{B} = B_0\left(\hat{i} + 2\hat{j} - 4\hat{k}\right)$ . If a test charge moving with a velocity $\vec{v} = v_0\left(3\hat{i} - \hat{j} + 2\hat{k}\right)$ experiences no force in that region, then the electric field in the region, in SI units, is:

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Answer: (d)

No force: $q\vec{E} + q\vec{v} \times \vec{B} = 0 \Rightarrow \vec{E} = -\vec{v} \times \vec{B}$ .
$(3\hat{i} - \hat{j} + 2\hat{k}) \times (\hat{i} + 2\hat{j} - 4\hat{k}) = (4 - 4)\hat{i} + (2 + 12)\hat{j} + (6 + 1)\hat{k} = 14\hat{j} + 7\hat{k}$
$\vec{E} = -v_0B_0(14\hat{j} + 7\hat{k})$
So the answer is (d).

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