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A long solenoid of cross-sectional area ...

A long solenoid of cross-sectional area `5.0 cm^2` is wound with 25 turns of wire per centimetre. It is placed in the middle of a closely wrapped coil of 10 turns and radius 25 cm as shown.


(a) What is the emf induced in the coil when the current through the solenoid is decreasing at a rate `-0.20 A//s` ?
(b) What is the electric field induced in the coil?

Text Solution

Verified by Experts

In the theory we have already derived mutual inductance between solenoid and coil
`M=(mu_0N_1N_2(piR_1^2))/l_1`
`=(mu_0N_1N_2S_1)/l_1`
`|e|=|M(di)/(dt)|=|(mu_0N_1N-2S_1)/l_1 (di_1)/(dt)|`
`=((4pixx10^-7)(25)(10)(5xx10^-4)(0.2))/10^-2`
`=3.14xx10^-6V`
b. `El=|(dphi)/(dt)|=e`
`:. E=e/l=e/(2piR_2)`
`=(3.14xx10^-6)/((2pi)(0.25))`
`=2xx10^-6V//m`
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