A particle of charge `+q` and mass `m` moving under the influence of as uniform electric field `Ehati` and uniform magnetic field `B hatk` follows trajectory form `P` to `Q` as shown in figure. The velocities at P and Q re `vhati and -2hatj`. Which of the following statement(s) is/are correct?

`a. E=3/4[(mv^2)/(qa)]`
b. Rate of work done by the electrif field at P is `3/4[(mv^3)/a]`
c. Rate of work done by the electric field at `P` is zero.
d. Rate of work done by both the field at `Q` is zero.

Explanation

Magnetic force done not work. From worm energy theorem:
`W_(F_e)=/_\KE`
E or `(qE)(2a)=1/2m[4v^2-v^2]`
or `E=3/4((mv^2)/(qa))`
`:.` Option a is correct
At `p`, rate of work done by electric field
`=F_e.v=(qE)(v)cos0^0`
`=q(3/4 (mv^2)/(qa))v=3/4((mv^3)/a)`
Threfore option b is also correct.
Rate of work done at `Q`
of electric field `=F_e.v=(qE)(2v)cos90^@=0` and of magnetic field is always zero. Therefore option `d` is also correct.