Question

A current I is flowing through the loop. The direction of the current and the shape of the loop are as shown in the figure. The magnetic field at the center of the loop is μ₀I/R time (MA = R,MB = 2R, ∠DMA = 90°)

(a)  5/16, but out of the plane of the paper.

(b)  5/16,  but int of the plane of the paper.

(b)  7/16,  but out of the plane of the paper.

(d)  7/16,  but int of the plane of the paper.

Answer 1

Correct option (d)  7/16,  but int of the plane of the paper.

Explanation:

 Magnetic field at the centre M due to current through the curved portion DA is

Magnetic field at the centre M due to current through the straight portion AB is B₂ = 0, since point M lies on the axis of the straight portion AB.

Magnetic field at the centre M due to current through the curved portion BC is

Magnetic field at the centre M due to current through the straight portion CD ts B₄ = 0, since point M lies on the axis of the stra:ight porlion CD.

The resultant magnetic field at the point M is