Q.In a compact coil of 50 turns, the current strength is 10A and the radius of the coil is 25×10⁻² meter. Find the magnitude of the magnetic field at its centre.

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 $B=\dfrac{\mu_0}{4\pi}\dfrac{I}{r}\theta$. …