A metal bar AB can slide on two parallel thick metallic rails separated by a distance l . A resistance R and an inductance L are connected to the rails as shown in the figure. A long straight wire, carrying a constant current I 0 is placed in the plane of the rails as shown. The bar AB is held at rest at a distance x 0 from the long wire. At t = 0 , it is made to slide on the rails away from the wire. It is observed that at time t = T , the metal bar AB is at a distance of 2 x 0 from the long wire and the resistance R carries a current i 1 . The net charge that has flown through resistance R from t = 0 to t = T is

Question

A metal bar AB can slide on two parallel thick metallic rails separated by a distance l . A resistance R and an inductance L are connected to the rails as shown in the figure. A long straight wire, carrying a constant current I 0 is placed in the plane of the rails as shown. The bar AB is held at rest at a distance x 0 from the long wire. At t = 0 , it is made to slide on the rails away from the wire. It is observed that at time t = T , the metal bar AB is at a distance of 2 x 0 from the long wire and the resistance R carries a current i 1 . The net charge that has flown through resistance R from t = 0 to t = T is, 1 R μ 0 l 2 π ln 2 - L i 1, 1 R μ 0 I 0 l π ln 2 - L i 1, 1 R μ 0 I 0 l 2 π ln 2 - L i 1, 1 R μ 0 I 0 2 π ln 2 - L i 1

MARKS App · Accepted Answer

Let v be velocity of AB when AB is at a distance x from the wire, e AB = B . ℓ . v = μ 0 I 0 2 π x I . v = d ϕ d t For circuit Loop, d ϕ d t - i R - L d i d t = 0 d ϕ d t - d q d t R - L d i d t = 0 ⇒ d q = d ϕ - L d i R Δ q = Δ ϕ - L Δ I R = 1 R [ ϕ 1 - ϕ 2 - L i 1 ] Δ q = 1 R [ μ 0 ℓ I 0 2 π ln 2 - L i 1 ]

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