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 ms –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

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 ms –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, 0 . 7 5 μ V, 1 μ V, 2 μ V, 0 . 5 μ V

MARKS App · Accepted Answer

d ϕ = μ 0 i 2 π y a dy ϕ = μ 0 i a 2 π ∫ x x + a dy y = μ 0 i a 2 π ln x + a - ln x E.m.f = - d ϕ dt = - μ 0 i a 2 π 1 x + a dx dt - 1 x dx dt = 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 r 1 - 1 r 2 V 1 = 2 × 10 - 7 × 1 ( 1 0.1 - 1 0.2 ) 10 × 0.1 = 10 - 6 v = 1 μ V

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