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. 8 N in -z-direction
C. 4N in z-direction
D. 8N in y-direction

Explanation

Here `q=-2muC=-2xx10^-6C`,
`vecB=2hatjT`, `vecv=(2hati+3hatj)xx10^6ms^-1`
Now force on charged particle, `vecF=q(vecvxxvecB)`
`=-2xx10^-6[(2hati+3hatj)xx10^6xx2hatj]`
`=-2xx10^-6xx10^6[(2hati+3hatj)xx(2hatj)]`
`=-2[4hatk][ As hatixxhatj=hatk, hatjxxhatj=0]`
`=-8hatk` [ 8N along -Z direction]