Question

Which of the following statements best describes Faraday's Law ?
A. The induced voltage in a coil is proportional to the number of turns in the coil and to the rate at which the magnetic field is changing.
B. The induced voltage in a coil is equal to the rate at which the magnetic field is changing.
C. The induced voltage in a coil is proportional to the number of turns in the coil and to the strength of the magnetic field.
D. The induced voltage in a coil is proportional to the number of turns in the coil and to the size of the magnetic field
E. The induced voltage in a coil proportional to the number of turns in the coil and to the source of the magnetic field.

Answer 1

Hint:According to Faraday's second law, the induced EMF is directly proportional to the rate of change of magnetic flux. So by finding a relation between magnetic flux and number of turns in a coil, we can find the relation among induced emf, rate of change of magnetic field and number of turns of a coil.

Complete answer:
Magnetic Flux: Magnetic flux is simply the number of magnetic lines passing through a particular area. It helps in determining the amount of magnetic field passing through a specific area. Mathematically it is given by the following equation:
\[\Phi =BAcos\theta \]
where \[\Phi \] is the magnetic flux, \[B\] is a magnetic field vector, \[A\] is the area vector and \[\theta \] is the angle between them.

The SI unit of magnetic flux is Weber (Wb). This formula implies that there will be maximum flux when the area is such that the area vector is parallel to the magnetic field lines. Flux is a scalar quantity because it is a dot product of two vectors. Note that in case of a coil with \[N\] turns, the flux is given by \[\Phi =(NA)B\]. Given that the cross sectional area of the coil\[A\] is parallel to the magnetic field passing through it.

Electromagnetic Induction:The phenomenon of inducing EMF when there is a change in magnetic flux is called Electromagnetic induction. It is based on Faraday's first law which states that whenever there is a change in magnetic flux, EMF will be induced and that EMF will last as long as change in flux continues. Now according to Faraday's second law of Electromagnetic induction, the EMF induced is directly proportional to the rate of change of the magnetic flux. So we can say that,
\[e\propto \dfrac{d\Phi }{dt}\]
Where \[e\] is the induced EMF and \[\Phi \] is the magnetic flux.

Now since \[e\propto \dfrac{d\Phi }{dt}\] and \[\Phi =(NA)B\]........(in case of a coil with N turns).
\[\Rightarrow ~\dfrac{d\Phi }{dt}=NA\dfrac{dB}{dt}\]
Hence the induced voltage is directly proportional to the number of turns of a coil and rate of change of magnetic field.

Therefore the ‘option A’ would be the best statement to describe Faraday's Law.

Note:Faraday’s law of electromagnetic induction, also known as Faraday’s law is the basic law of electromagnetism which helps us to predict how a magnetic field would interact with an electric circuit to produce an electromotive force (EMF). This phenomenon is known as electromagnetic induction.