The wire loop PQRSP formed by joining two semicircular wire of radii R₁ and R₂ carries a current I as shown. The magnitude of the magnetic field at the centre ' 0 ' is

Step-by-step solution

The magnetic field at center O arises solely from the semicircular arcs QR and SP , as the straight segments PQ and RS contribute nothing when O lies along their axes. For arc QR with radius R₁ , the field is B_ QR = ₀ I 4 R₁ directed into the page. For arc SP with radius R₂ , it is B_ SP = ₀ I 4 R₂ directed out of the page. Since these fields oppose and R₂ B_ QR , the net field is B_ net = ₀ I 4 ( 1 R₂ - 1 R₁ ) out of the page. The magnitude is ₀ I 4 ( 1 R₂ - 1 R₁ ) .