A rectangular loop of width b = ( e − 1 ) a , length l , mass m resistance R is placed closed to and coplanar with a very long fixed straight conductor carrying I 0 . The current in the conductor is

Question

A rectangular loop of width b = ( e − 1 ) a , length l , mass m resistance R is placed closed to and coplanar with a very long fixed straight conductor carrying I 0 ​ . The current in the conductor is suddenly switched off. Velocity of loop after current is switched off, is (e is exponential)

TestHub · Accepted Answer

ϕ = 2 π μ 0 ​ I ( t ) ​ i = R 1 ​ ( Δ t Δ ϕ ​ ) = R 2 π μ 0 ​ l ​ d t d I ​ B ( i ) ​ B ( ii ) ​ ∴ F ( t ) f ( t ) ∴ m v 0 ​ ∴ v 0 ​ ​ = 2 πa μ 0 ​ I ​ = 2 πa e μ 0 ​ I ​ = i l ( B 1 ​ − B 2 ​ ) = 2 π i l μ 0 ​ I ​ ( a 1 ​ − a e 1 ​ ) = 2 π i l μ 0 ​ I ​ a e ( e − 1 ) ​ = 2 πa e μ 0 ​ I l ( e − 1 ) ​ 2 π R d t μ 0 ​ l d I ​ = ∫ F d t = 4 π 2 R a e μ 0 2 ​ l 2 ( e − 1 ) ​ ∫ I 0 ​ 0 ​ I d I = 8 π 2 m R a e μ 0 2 ​ I 0 2 ​ l 2 ( e − 1 ) ​ ​

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JEE Advanced (2028)