The magnetic force acting on a charged particle of charge `-2 muC` in a magnetic field of `2 T` acting `y` direction, when the particle velocity is `(2i + 3 hat(j)) xx 10^(6) ms^(-1)`, is

Options

A. `8 N` in `-z` direction
B. `4 N` in `z` direction
C. `8 N` in `y` direction
D. `8 N` in `z` direction

Answer

A

Explanation

`vec(B) = 2 hat(j)T, vec(v) = (2 hat(i) + 3 hat(j)) xx 10^(6) m//sec, q = -2 xx 10^(-6) C`
`vec(F)_(m) = q vec(v) xx vec(B)`
`= (-2 xx 10^(-6))[(2 hat(i) + 3 hat(j)) xx 10^(6)] xx [2 hat(j)]`
`= - 8 hat(k) N`
i.e. `8 N` along -z direction