A ring of radius `R` having a linear charge density `lambda` moves towards a solid imaginary sphere of radius `(R)/(2)`, so that the centre of ring passes through the centre of sphere. The axis of the ring is perpendicular to the line joining the centres of the ring and the sphere. The maximum flux through the sphere in this process is

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))`,.