Physics - Magnetism Question with Solution | TestHub

The magnetic field at the centre of a circular arc subtending an angle $\theta$ is given by $B=\frac{{\mu }_{0}I}{4\pi R}\theta$.

For an arc which is $\frac{3}{4}$ of the circumference, the angle subtended at the centre is $\theta =\frac{3}{4}\times 2\pi =\frac{3\pi }{2}$.

Substituting $\theta$ in the formula:

$B=\frac{{\mu }_{0}I}{4\pi R}\times \frac{3\pi }{2}=\frac{3{\mu }_{0}I}{8R}$

Since the current flows in the anticlockwise direction, by the right-hand thumb rule, the direction of the magnetic field at the centre is upward (perpendicular to the plane and pointing outwards).

Therefore, the magnetic field is $\frac{3{\mu }_{0}I}{8R}$ in the upward direction.

Answer: $\frac{3{\mu }_0\mathrm{I}}{8\mathrm{R}}$ in upward direction