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Question

Two circular coils of radii 5.0 cm and 10 cm carry equal currents of 2.0 A. The coils have 50 and 100 turns respectively and are placed in such a way that their planes as well as the centres coincide. Find the magnitude of the magnetic field B at the common centre of the coils if the currents in the coils are (a) in the same sense (b) in the opposite sense.

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Solution

No. of turns: n1 = 50 and n2 = 100
Magnitude of currents: i1 = i2 = 2 A
Radii of loops: r1 = 5 cm and r2 = 10 cm
(a) In the same sense:

The magnetic field intensity at the centre is given by
B = μ0n1i12r1+μ0n2i22r2= 4π×10-7×50×22×5×10-2+4π×10-7×100×22×10×10-2= 4π×10-4+4π×10-4= 2×4π×10-6= 8π×10-3 T

(b) In the opposite sense:
The magnetic field intensity at the centre is given by

B = μ0n1i12r1-μ0n2i22r2 =4π×10-7×50×22×5×10-2-4π×10-7×100×22×10×10-2 =0

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