A loop of wire is situated inside a large solenoid, with the plane of the loop i

Question

A loop of wire is situated inside a large solenoid, with the plane of the loop initially perpendicular 15) to the axis of the solenoid. Current can be made to flow through the loop of wire if

A) the loop of wire is rotating within the solenoid, and a constant current is flowing through the solenoid wire.

B) a constant current is flowing through the solenoid wire.

C) the current flowing through the solenoid is decreasing with time.

D) All of the above statements are true.

E) Only two of the above statements are true.

Explanation / Answer

for a current to be there in the loop ,
an induced EMF must be present in the loop.

And
induced EMF = rate of change of flux w.r.t time

so,

Flux must be changing wrt time in order to induce emf

And Flux = BA cos theta and for a solenoid , B = mu* n*I

Now,

for option A) as loop is rotating , and the current in the solenoid is constant ,

so ,B is constant and theta ( and hence cos theta) is changing .
so ,

the flux is changing wrt time

so ,

(A) is correct

now,

for ( B) if constant current is flowing through wire ( which means constant B ), and there is no movement given for loop ,

so ,
flux is constant.
Therefore , there will no EMf induced and hence there will be no current in the loop

so , ( B) is incorrect

for (C) as current in solenoid is itself changing , so , B ( = mu* n* I ) must be changing as well.

so,
flux is changing wrt time.
Therefore , there will EMf induced and hence there will be current in the loop.

(C) is correct

As

both ( A) and (C) are correct ,

so final answer would be (E) i.e, Only two of the above statements are true.

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