Magnetic Effects & Magnetism

JEE Main level, single correct, medium

228 of 276

Question 228 of 276

In a certain region static electric and magnetic fields exist. The magnetic field is given by B⃗=B0(i^+2j^−4k^)\vec{B}={B}_{0}\left(\hat{i}+2\hat{j}-4\hat{k}\right). If a test charge moving with a velocity v⃗=v0(3i^−j^+2k^)\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) E⃗=−v0B0(14j^+7k^)\vec{E}=-{v}_{0}{B}_{0}\left(14\hat{j}+7\hat{k}\right)

The total force experienced by test charge is Fe⃗+F⃗m=0\vec{{F}_{e}}+{\vec{F}}_{m}=0.

Fe=−Fm{F}_{e}=-{F}_{m}

Fe=−q0v0B0(V⃗×B⃗){F}_{e}=-{q}_{0}{v}_{0}{B}_{0}\left(\vec{V}\times \vec{B}\right)

Fe=−q0v0B0[(3i^−j^+2k^)×(i^+2j^−4k^)]{F}_{e}=-{q}_{0}{v}_{0}{B}_{0}\left[\left(3\hat{i}-\hat{j}+2\hat{k}\right)\times \left(\hat{i}+2\hat{j}-4\hat{k}\right)\right]

F⃗e=−qv0B0(14j^+7k^){\vec{F}}_{e}=-q{v}_{0}{B}_{0}(14\hat{j}+7\hat{k})

The electric field produced by the test charge is ∵E⃗=f⃗eq=−v0B0(14j^+7k^)∵\vec{E}=\dfrac{{\vec{f}}_{e}}{q}=-{v}_{0}{B}_{0}(14\hat{j}+7\hat{k})

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