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Two Concentric Circular Loops of Radius 1 Cm and 20 Cm Are Placed Coaxially. (I) Find Mutual Inductance of the Arrangement. (Ii) If the Current Passed Through the Outer Loop is Changed at a Rate - Physics

Numerical

Two concentric circular loops of radius 1 cm and 20 cm are placed coaxially.
(i) Find mutual inductance of the arrangement.
(ii) If the current passed through the outer loop is changed at a rate of 5 A/ms, find the emf induced in the inner loop. Assume the magnetic field on the inner loop to be uniform.

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Solution

We know `varphi = "MI"`

And magnetic field at the center of the bigger loop `vec"B" = (mu_o"I")/(2"R") = (4pi xx 10^-7"I")/(2xx20xx10^-2) = pi xx 10^-6"I"`

Flux through the smaller loop

`varphi = "BA"_"s" = (4pixx10^-5"I")/40 xx pi(0.01)^2 = pi^2 xx 10^-10 xx "I"`

`"M" = varphi/"I" = pi^2 xx 10^-10 = 9.86 xx 10^-10 "H"`

Now emf induced

e = `-("d"varphi)/("d""t") = -9.86 xx 10^-10 xx ("d""I")/("d""t")`

e = `-9.86 xx 10^-10 xx 5 = -4.93 xx 10^-9  "V"`

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