A ring of radius R having a linear charge density λ moves towards a solid imaginary sphere of radius R2,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. If the maximum flux through the sphere in this process is found to be λπRnϵ0, , find the value of n.

Electric flux will be maximum when maximum length of ring isinside the sphere. This will occur when the length of the chord AB is maximum. Now maximum length of chord AB can be the diameter of the ring. In this case the arc of ring inside the sphere subtends an angle of π/3 at the centre of ring. Thus charge on this arc in this situation is given asq=Rπ3⋅λ⇒ϕ=Rπ3λϵ0=Rπλ3ϵ0