Q.A circular coil of wire is made up of 100 turns, each of radius 8.0 cm. If a current of 0.40 A passes through it, what will be the magnetic field at the centre of the coil?

Applying the Biot-Savart law to a circular arc of wire exploits a special geometric fact unique to circles: every current element along the arc is always exactly perpendicular to the radius vector drawn to the centre, and every element is the same fixed distance from the centre. This simplifies the Biot-Savart integral for the field at the centre O of an arc of radius r subtending angle $\theta$ (in radians) to $B=\dfrac{\mu_0}{4\pi}\dfrac{I}{r}\theta$. …