In the figure a charged small sphere of mass `m` and the charge `q` starts sliding from rest on a vertical fixed circular smooth track of radius `R` from the position `A` shown. There exist a uniform magnetic field of `B`. Find the maximum force exerted by track on the sphere during its motion.

Options

A. `N_(max)=2mg+qBsqrt(2gR)`
B. `N_(max)=3mg+qBsqrt(2gR)`
C. `N_(max)=3mg+2qBsqrt(2gR)`
D. `N_(max)=3mg+qBsqrt(gR)`

Answer

B

Explanation

Maximum force will be at lowest point.

Magnetic force will not do any work.
velocity at lowest point : `v=sqrt(2gR)`
`N-mg-qvB=ma_(c) implies N=mg+(mv^(2))/R+qvB`
`implies N=3mg+qBsqrt(2gR)`