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.

Options

A. (i), (ii)
B. (ii), (iv)
C. (i), (ii), (iv)
D. (i), (iv)

Answer

C

Explanation

(i) Work is done only by electric force.
By work-energy theorem between `P` and `Q`
`Delta W = K_(2) - K_(1) = K_(Q) - K_(P)`
`qE xx 2a = (1)/(2)m(2v^(2)) - (1)/(2)mv^(2) = (3)/(2)mv^(2)`
`E = (3mv^(2))/(4qa)`, (i) is O.K.
(ii) `P = vec(F)_(e). vec(v) = qvec(E).vec(v) = q(Ehat(i)).(v hat(i)) = qEv`
(iv) Work done by magnetic force is always force is always zero
At `Q`, `F_(e)_|_^(ar)v, P = 0`
(iv) is O. K.