A hollow non conducting sphere of radius `R` has a positive charge `q` uniformly distributed on its surface. The sphere starts rotating with a constant angular velocity `'omega'` about an axis passing through center of sphere, as shown in the figure. Then the net magnetic field at center of the sphere is

Options

A. `(mu_(0)qomega)/(2piR)`
B. `(mu_(0)qomega)/(3piR)`
C. `(mu_(0)qomega)/(6piR)`
D. `(mu_(0)qomega)/(12piR)`

Answer

C

Explanation

Magnetic field due to the ring on its axis is
`B=(mu_(0)pir^(2)i)/(2pi(r^(2)+x^(2))/(3//2))` (due to ring)
`B=int_(-pi//2)^(+pi//2)(mu_(0)pi(Rcostheta)^(2)((2piRcos theta R d theta sigma)/(2pi//omega)))/(2pi[(Rcostheta)^(2)+(Rsintheta)^(2)]^(3//2))`
Where `sigma=q/(4piR^(2))`
`B=(mu_(0)qomega)/(6piR)`