Module 3 : MAGNETIC FIELD
Lecture 19 : Mutual Inductance
  Example 23 :
  By considering the current in $C_2$to be time varying determine the change in flux of the larger coil and hence determine the mutual inductance.
Solution :
  Since the field over the larger loop cannot be considered uniform, we need to use expressions for the magnetic field due to a magnetic dipole. The field is conveniently expressed in terms of its radial and tangential components. For a point dipole, the field components are given by expressions similar to the ones we derived for electric dipole. By replacing the electric dipole moment $p$by the magnetic dipole moment $\mu$and permittivity factor $1/4\pi\epsilon_0$by the permeability of vacuum $\mu_0/4\pi$, we have
 
\begin{eqnarray*} B_r &=& \frac{\mu_0}{4\pi}\frac{2\mu\cos\theta}{r^3}\\ B_\theta &=& \frac{\mu_0}{4\pi}\frac{\mu\sin\theta}{r^3} \end{eqnarray*}
  In the figure, the plane of the loop is normal to the page and the current direction is anticlockwise as seen from the right, so that the magnetic moment vector is as shown.

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