A particle of charge \( +\mathrm{q} \) and mass \( \mathrm{m} \) moving under the influence of a....

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A particle of charge \( +\mathrm{q} \) and mass \( \mathrm{m} \) moving under the influence of a uniform electric field \( E \hat{i} \) and a
\( \mathrm{P} \)
uniform magnetic field \( B \hat{k} \) follows a trajectory from \( \mathrm{P} \) and \( \mathrm{Q} \) as shown in figure. The velocities at \( \mathrm{P} \) and \( \mathrm{Q} \) are \( v \hat{i} \) and \( -2 v \hat{j} \). Which of the following statement(s) is/are correct?
(1) \( E=\frac{3}{4}\left(\frac{m v^{2}}{q a}\right) \)
(2) Rate of work done by the electric field at \( \mathrm{P} \) is \( \frac{3}{4}\left(\frac{m v^{3}}{a}\right) \)
(3) Rate of work done by the electric field at P is zero
(4) Rate of work done by both fields at \( Q \) is zero.


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