A charged particle of mass 'm' and charge 'q' moving under the… | JEE Main 2020 (9 Jan, Shift 1)

Q83JEE Main 2020 · 9 JAN · SHIFT 1Difficult

Moving Charge in a Magnetic Field

A charged particle of mass 'm' and charge 'q' moving under the influence of uniform electric field $E\hat{i}$ and a uniform magnetic field $B\hat{k}$ follows a trajectory from point P to Q as shown in figure. The velocities at P and Q are respectively, $v\hat{i}$ and $-2v\hat{j}$ . Then which of the following statements (A, B, C, D) are correct?

(Trajectory shown is schematic and not to scale):

(A) E = $\frac{3}{4}\left(\frac{mv^2}{qa}\right)$

(B) Rate of work done by the electric field at P is $\frac{3}{4}\left(\frac{mv^3}{a}\right)$

(D) The difference between the magnitude of angular momentum of the particle at P and Q is 2mav.

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Answer: (b)

(A) Only $\vec{E}$ does work, over $\Delta x = 2a$ : $qE(2a) = \tfrac{1}{2}m(4v^2 - v^2) \Rightarrow E = \dfrac{3}{4}\dfrac{mv^2}{qa}$ . Correct.
(B) Power at P: $qEv = \dfrac{3}{4}\dfrac{mv^3}{a}$ . Correct.
(C) At Q, $\vec{v} = -2v\hat{j} \perp \vec{E}$ , and the magnetic force never does work, so total power is zero. Correct.
(D) About O: $L_P = mva$ , $L_Q = m(2v)(2a) = 4mva$ ; difference $= 3mva$ , not $2mva$ . Wrong.
So the answer is (b) (A), (B), (C).

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