This question is attempting to simulate the process of a circular particle accelerator. We are given a constant electric field $E$ along the angular direction and a varying magnetic field $B$ along the perpendicular direction so that the radius of the orbit of the particle is always being limited to be $R$. Now assuming the charged particle has mass $m$ and charge $q$, we are asked what is $\frac{v}{c}$ with respect to t. I have difficulty deriving such a relation and I know the following equation $$ \frac{dp}{dt}=m\frac{d\gamma v}{dt}=qvB+qE $$ could help. However, it can't lead me to my expected result. Therefore I wonder if anyone can give me a hint on how to work out the desired result.

Thanks.