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The magnetic field induction at the centre of a current-carrying circular coil (coil 1) and a closed coil (coil 2), shaped as a quarter of a disc is found to be equal in magnitude. If both the coils have equal area, then find the ratio of the currents flowing in coil 2 and coil 1.

Correct answer

8

Step-by-step solution

Let r and x be the radius of circular and quarter circular coil, then πr 2 = πx 2 4         ⇒ x = 2 r . μ 0 4 π 2 πI r = μ 0 4 π π 2 I ' x   ⇒ I ' I = 4 x r = 8

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