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A particle of charge 'q' and mass 'm' en...


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

A

`(pim)/(qB)`

B

`(pim)/(2qB)`

C

`(pim)/(3qB)`

D

`(pim)/(4qB)`

Text Solution

Verified by Experts

The correct Answer is:
C
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)`
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