Question

The induced emf produced when a magnet is inserted into a coil does not depend upon:
A. The number of turns in the coil
B. The resistance of the coil
C. The speed of approach of the magnet
D. All the above

Answer 1

Hint: The above problem can be resolved using the magnetic flux concepts and applications and the relation for the magnetic flux and the induced emf. The mathematical formula for the induced emf is used, such that this formula directly relates the number of turns and the rate of change of the magnetic flux.

Complete step by step solution:
The expression for the induced emf produced when a magnet is inserted into a coil is,
\[\varepsilon = N \times \left( {\dfrac{{d\phi }}{{dt}}} \right)\]
Here, N denotes the number of turns and \[\left( {\dfrac{{d\phi }}{{dt}}} \right)\] denotes the rate of change of the magnetic flux.
With the reference from the above formula, the option A is not correct because the magnitude of induced emf varies directly with the number of turns N.
But in option (B), the resistance is used to relate the induced emf. And according to the expression of the induced emf, there is no significance of resistance of coil, relating with the induced emf. Hence, the induced emf produced does not depend on the resistance of coil and option (B) satisfies the statement.
The option (C) is incorrect because the emf depends directly on the magnetic flux. And this magnetic flux depends on the magnitude of the external magnetic field. Which in turn is dependent on the magnetic moment.
Therefore, the induced emf produced when a magnet is inserted into a coil does not depend upon the resistance of the coil and option (B) is correct.

Note:
To resolve the given problem, one must remember the basic mathematical formula for the induced emf and its relation with the coil's resistance.