Question

A magnet is moved towards the coil, first quickly and then slowly. The induced e.m.f. produced is:
A. Larger in first case
B. Smaller in first case
C. Equal in both case
D. Larger or smaller depending upon the resistance of the coil

Answer 1

The change in flux according to the movement of the magnet is the key point here. Faraday’s law and Lenz law will give an idea to proceed with the question. Also, the direction of the induced e.m.f will be decided by the movement of the magnet. The varying magnetic field due to motion of the magnet induces an e.m.f.

Complete step by step solution:
A magnet consists of North and South poles. Magnetic field lines are used to visually represent the magnetic field of a magnet. They are the continuous closed loops which direct from the North Pole to the South Pole. The number of magnetic field lines crossing per unit area determines the strength of the magnetic field. The larger the magnetic field lines, the stronger the magnetic field,$B$ .
The number of magnetic field lines passing through a closed surface area is called flux, $\phi$ . Weber or Tesla meter squared is the SI unit of flux. Flux is a scalar quantity. It is represented by:
$\phi =B.A=BA\cos \theta$
Where $B=$ uniform magnetic field
$A=$ area of the closed loop
$\theta =$ angle between $B$ and $A$
Faraday’s Law stated that the magnitude of emf induced in a circuit is equal to the time rate of change of magnetic flux through the circuit.
$\varepsilon =\dfrac{-d\phi }{dt}$
The negative sign represents that the direction of the induced emf is opposite to the direction of the rate of change of flux.
The flux through a coil can be changed if:
The loop moves in a permanent magnetic field.
Coil is at rest in a varying magnetic field
The shape of the coil is changed in a magnetic field.
According to the question, first the magnet moves quickly, imparting maximum number of magnetic field lines in a short time. This implies that the rate of change of flux is maximum in this case and hence the induced emf will be larger. If the magnet moves slowly, the rate of change of flux will be less and hence induced emf is less.
Therefore, option A is correct.

Note:
Lenz’s Law tells about the direction of the induced emf. It states that the polarity of induced emf is such that it produces a current which opposes any change in the magnetic flux that produced it. Electromagnetic induction can be used to develop devices like AC generators, transformers etc.