Question

A long straight conductor is bent into shape as shown. If it carries 1A and its radius is R, then magnetic field B at the centre of circular coil

• A. $\infty$
• B. Zero
• C. $\frac{{\mu }_{0}i(\pi +1)}{2\pi R}$
• D. $\frac{{\mu }_{0}i(\pi -1)}{2\pi R}$

Answer 1

The correct option is D $\frac{{\mu }_{0}i(\pi -1)}{2\pi R}$

The magnetic field due to straight infinite wire part $=\frac{{\mu }_{0}i}{2\pi R}$ outside the plane.

Magnetic field due to bent loop part $=\frac{{\mu }_{0}i}{2R}$ into the plane.

Thus net magnetic field at the center $=\frac{{\mu }_{0}i}{2\pi R}(\pi -1)$.