A magnetic dipole of moment M = mz is located at the origin. A thin circular conducting ring of radius a vibrates such that the position of its centre is r = [z_{0} + b cos (ωt)]z with b << a < 20. The plane of the ring remains parallel to the x—y plane during the vibration. Find the emf around the ring in the φ direction.

**So, The magnetic field of the dipole is**

**B (r) = ****μ _{0 /} 4π [ {3r (m.r) – r^{2}m} / r_{5}]**

Since b << a < z_{0} we can approximate the magnetic field anywhere on the ring as it vibrates by

Where, **z _{r}(t) = [z_{0} + b cos (ωt)]z**, is the height of the ring.

The magnetic flux through the loop is:

Since **a << z _{0}**. Hence,

**Ɛ = – (dφB / dt)**

So, **Ɛ ≈ – [ 3μ _{0}ma^{2}bω / 2z_{0}^{4}] sin (ωt)**

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