A uniform magnetic field of magnitude 0.20 T exists in space from east to west what speed should a particle of mass 0.010 g and having a charge `1.0 X 10^(-5)C` be projected from south to north so that it moves with a uniform velocity?

Options

A. `49 m//sec`
B. `49.5 m//sec`
C. `50 m//sec`
D. `48.5 m//sec`

Answer

C

Explanation

Since velocity is constant i.e. net force on particle is zero. The magnetic force is balanced by weight
`vec(B) = -0.2 hat(i), vec(v) = v hat(j)`
`vec(F)_(m) = q(v hat(j) xx -0.2 hat(i)) = 0.2 q v hat(k) = 0.2 xx 10^(-5) v hat(k)`

`Bqv = mg`
`v = (mg)/(Bq) = (0.01 xx 10^(-3) xx 10)/(0.2 xx 10^(-5)) = 50 m//sec`