A particle of charge +q and mass m moving under the influence of a uniform electric field \[E\hat{i}\] and a uniform magnetic field \[B\hat{k}\] follows trajectory from P to Q as shown in figure. The velocities at P and Q are \[v\hat{i}\] and \[-2v\hat{j}\] respectively. Which of the following statement(s) is/are correct [IIT 1991; BVP 2003]

• A.            \[E=\frac{3}{4}\frac{m{{v}^{2}}}{qa}\]
• B.            Rate of work done by electric field at P is \[\frac{3}{4}\frac{m{{v}^{3}}}{a}\]
• C.            Rate of work done by electric field at P is zero
• D.            Rate of work done by both the fields at Q is zero