A square frame of side 10 cm and a long straight wire carrying current 1 A are in the plane of the paper. Starting from close to the wire, the frame moves towards the right with a constant speed of 10

Question

A square frame of side 10 cm and a long straight wire carrying current 1 A are in the plane of the paper. Starting from close to the wire, the frame moves towards the right with a constant speed of 10 m s - 1 (see figure). The e.m.f induced at the time the left arm of the frame is at x = 10 cm from the wire is

TestHub · Accepted Answer

d ϕ = μ 0 i 2 π y a d y ϕ = μ 0 i a 2 π ∫ x x + a d y y = μ 0 i a 2 π l n x + a - l n x E.m.f =- d ϕ d t = - μ 0 i a 2 π 1 x + a d x d t - 1 x d x d t = μ 0 i a 2 π a . v x x + a = μ 0 2 π . i a 2 v x x + a = 2 × 10 - 7 × 1 × 0.1 2 × 10 0.1 × 0.2 = 1 μ V Alternative method: Consider two sides which are perpendicular to the velocity as case of motional e.m.f. E = E 1 - E 2 = B 1 – B 2 V l = μ 0 I 2 π 1 x - 1 x + a V l = 2 × 10 - 7 × 1 1 0.1 - 1 0.2 × 10 × 0.1 = 10 - 6 V = 1 μ V

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