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

When a charge `q` moves with velocity `vec(v)` inside magnetic field of strenght `vec(B)`, then force on charge is called magnetic Lorentz force. The magnetic Loretz force is in the direction of vector `vec(V) xx vec(B)`.
Magnetic Lorentz force `vec(F) = q(vec(V) xx vec(B))`
`= -2xx10^(-6)[2xx2xx10^(6)]`
`= 8 N` along negative z -axis