Q.State the formula for magnetic induction produced by a current in a circular arc of a wire. Hence find the magnetic induction at the centre of a current carrying circular loop.

The Biot–Savart law gives the field of a circular arc directly proportional to the angle it subtends; a full circular loop is the special case $\theta = 2\pi$.

By the Biot–Savart law, the magnetic field at the centre of a circular arc of radius $r$, carrying current $I$, subtending angle $\theta$ (in radians) at the centre, is

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

For a complete circular loop, the arc subtends the full angle $\theta = 2\pi$ at the centre, so

$B = \dfrac{\mu_0 I}{4\pi r}\times 2\pi = \dfrac{\mu_0 I}{2r}$

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