A ring is of the shape of a hoola-hoop of negligible thickness. A ring of radius \( R \) carries a current \( I \). Prove that the magnetic field at a given point in the plane of the ring at a distance \( a \) from the center, due to the magnetic field of the ring, is \[ B = \dfrac {\mu_0}{2\pi} \cdot IR \cdot \displaystyle\int_{0}^{\pi} \dfrac {R - a \cos \theta}{\sqrt{\left( a^2 + R^2 - 2aR \cos \theta \right)^3}} \, \mathrm{d}\theta. \]

**Note**: This problem originally appeared on the IPhOO.

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