A charged particle with charge to mass ratio `((q)/(m)) = (10)^(3)/(19) Ckg^(-1)` enters a uniform magnetic field `vec(B) = 20 hat(i) + 30 hat(j) + 50 hat(k) T` at time t = 0 with velocity `vec(V) = (20 hat(i) + 50 hat(j) + 30 hat(k)) m//s`. Assume that magnetic field exists in large space.
The pitch of the helical path of the motion of the particle will be

Options

A. `pi//100m`
B. `pi//125m`
C. `pi//215m`
D. `pi//250m`

Answer

D

Explanation

Pitch= TV cos `theta`
`=(1)/(f)V(vec(V)vec(B))/(BV)=(pisqrt(38)xx400)/(10^(4)sqrt(3800))=(4pi)/(10^3)m=(pi)/(250)m`.