In figure, there are two semi-circle of radii $r_{1}$ and $r_{2}$ in which a current i is flowing. Find the magnetic induction at centre O.

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Solution

$B = B_{1} + B_{2} = \frac{μ_{0}}{4 π} \times \frac{π i}{r_{1}} + \frac{μ_{0}}{4 π} \times \frac{π i}{r_{2}}$ $= \frac{μ_{0} i}{4} [\frac{1}{r_{1}} + \frac{1}{r_{2}}] = \frac{μ_{0} i}{4} [\frac{r_{1} + r_{2}}{r_{1} r_{2}}]$

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