A ring of radius R having a linear charge density moves towards a solid imaginary sphere of radius `(R)/(2)` , so that the centre of ring pass though the centre of sphere. The axis of the ring is perpendicular

Options

A. `(lambdaR)/(in_(0))`
B. `(lambdaR)/(2in_(0))`
C. `(lambda piR)/(4 in_(0))`
D. `(lambda piR)/(3in_(0))`

Answer

D

Explanation

Flux will be maximum when maximum length of ring is inside the sphere

This will occur when the chord AB is maximum Now maximum length of chord AB = diameter of sphere in this case the arc of ring inside the sphere subtends an angle of `(pi)/(3)` at the centre of ring.
change on this arc `= (R pi)/(3) lamda`
`phi = ((R pi)/(3)lamda)/(in_(0))=(R pi lamda)/(3 in_(0))`,.