As shown in figure, a long wire kept vertically on the plane of paper carries electric current-I. A conducting ring moves towards the wire with velocity v with its plane conducting with the plane of paper. Find the induced emf produced in the ring when it is at a perpendicular distance r from the wire. Radius of the ring is a and a `lt lt` r.

Explanation

Magnetic field at a distance r from the wire carrying current is `B =(mu_0I)/(2pir)`
`therefore` Magnetic flux linked with the ring,
`phi=B(pia^2)`
`=(mu_0I)/(2pir)xxpia^2`
`=(mu_0Ia^2)/(2r)`
`therefore` emf `epsilon=-(dphi)/(dt)`
`=-d/(dt)((mu_0Ia^2)/(2r))`
`=(mu_0Ia^2)/2 (1/r^2)(dr)/(dt)`
`therefore epsilon = (mu_0Ia^2)/(2r^2) v (because (dr)/(dt)=v)`