Correct Answer - A
R=`(mv)/(qB)` ltBrgt `sintheta=(R)/(sqrt(2)xxR)=(1)/(sqrt(2)), theta=45^(@)`
After coming out of B q will collide with the wall
time to exit B
`t_(1)=(pim)/(4qB)`
time to travel in region where B is absent is `t_(2)`
`(R)/(sqrt(2)s)=cos45`
s=R
`t_(2)=(s)/(v)=(R)/(v)=(mv)/(vqB)=(m)/(qB)` ltBrgt total time = `2t_(2)=(2m)/(qB)` ltBrgt time for returing journey in B
`t_(3)=(pim)/(4qB)` ltBrgt total time = `(pim)/(4qB)+(pim)/(4qB)+2q(m)/(qB)`
`(m)/(qB)[(pi)/(2)+2]=(m)/(2qB)[pi+4]`