A square conducting loop of side length L carries a current I . The magnetic field at the centre of the loop is

Question

A square conducting loop of side length L carries a current I . The magnetic field at the centre of the loop is, independent of L, proportional to L 2, inversely proportional to L, linearly proportional to L

MARKS App · Accepted Answer

Field due to wire AB at the center, B A B = μ 0 I 4 π L 2 sin ⁡ 4 5 ° + sin ⁡ 4 5 ° B c e n t e r = 4 B A B B c e n t e r = 4 μ 0 I 4 π L 2 1 2 + 1 2 B c e n t e r = 2 2 μ 0 I π L B c e n t e r ∝ 1 L

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