A particle of charge 'q' and mass 'm' enters a uniform magnetic field region `vecB=-Bhatk` at origin 'O' with a velocity `vecv_(0)=6hati` m/s and after some time it exist the magentic field region with a velocity `vecv=(3hati+3sqrt(3))`m/s as shown. The time interval for which the particle has moved in the magnetic field region is

Options

A. `(pim)/(qB)`
B. `(pim)/(2qB)`
C. `(pim)/(3qB)`
D. `(pim)/(4qB)`

Answer

C

Explanation

Since the particle exists the magnetic field region with a velocity `vecv=(3hati+3sqrt(3)hatj)m//s`
`tantheta=(3sqrt(3))/(3)`
`thereforetheta=(pi)/(3)`
The angular displacement of the particle in the magnetic field region is `theta=(pi)/(3)`
Angular velocity `omega=(qB)/(m)`
`thereforet=(theta)/(omega)=(pim)/(3qB)`