Question

Figure shows a semi circular coil of radius z along with long straight wires. When a current I flows through this set up, the magnetic field, at O, the centre of semi circular arc, equals

(1) \(\frac{μ_0i}{4\pi Z}(\frac{\pi}{2}-2)\)outwards

(2) \(\frac{μ_0i}{4\pi Z}(\pi + 2)\) outwards

(3) \(\frac{μ_0i}{4\pi Z}({\pi - 2})\)into the plane of the paper

(4) \(\frac{μ_0i}{4\pi Z}({\pi +2})\) into the plane of the paper

Answer 1

(3) \(\frac{μ_0i}{4\pi Z}({\pi - 2})\)into the plane of the paper

Magnetic field, due to semi circular portion, is given by

Now the the point O is at a distance z from the straight conductor P of infinite length.

Also, the magnetic field at point O due to infinite long straight conductor Q, is given by

Hence the resultant field