Question

Faraday’s second law of electromagnetic induction states that:
A. The magnitude of the induced emf is directly proportional to the rate of change of flux
B. The magnitude of the induced emf is inversely proportional to the rate of change of flux
C. The direction of the induced emf is such that it opposes the change in flux
D. The magnitude of the induced emf is directly proportional to the square of the rate of change of flux.

Answer 1

Hint: Changing magnetic flux produces an emf in a closed circuit. To get the answer easily, you can think of the applications of Faraday’s law like transformers, inductors, electrical motors, generators etc.
Formula used: \[e=N\dfrac{d\Phi }{dt}\], where \[\dfrac{d\Phi }{dt}\] is the change in magnetic flux, N is the number of turns of the coil and e is the induced emf.

Complete step by step answer:
 Faraday’s second law of electromagnetic induction states that the magnitude of induced emf in a closed circuit is directly proportional to the rate of change of magnetic flux linked with the circuit.
So the correct option is A.
\[e=\dfrac{d\Phi }{dt}\], where \[\dfrac{d\Phi }{dt}\] is the change in magnetic flux, N is the number of turns in the coil and e is the induced emf.
Additional information: We can derive the formula of Faraday’s second law.
Consider a bar magnet, that is approaching towards the magnet. If we are considering two instants of time, then the flux linkage with the coil will be different for each time.
So the flux linkage with the coil at the time \[{{T}_{1}}\] will be,
\[{{T}_{1}}=N{{\phi }_{1}}\] , where N is the number of turns of the coil.
The flux linkage with the coil at the time \[{{T}_{2}}\] will be,
\[{{T}_{2}}=N{{\phi }_{2}}\]
Therefore the change in flux will be at a particular time,
\[{{T}_{2}}-{{T}_{1}}=N({{\phi }_{2}}-{{\phi }_{1}})\]
We can indicate this change in flux as \[\Phi \]
\[({{\phi }_{2}}-{{\phi }_{1}})=\Phi \]
So the change in flux linkage for N turns will be \[N\Phi \]
Take the derivative of this concerning the time. Here the flux is only varying with the time. Thus,
\[\Rightarrow N\dfrac{d\Phi }{dt}\]
This rate of change of magnetic flux is the induced emf on the circuit. So we can write as,
\[e=N\dfrac{d\Phi }{dt}\]
According to Faraday’s law of electromagnetic induction, the rate of change of magnetic flux linkage will be equal to the induced emf.
The negative sign indicates that the induced emf is opposing the change of magnetic flux. This indicates the Lenz law.
 We can increase the induced emf;
1. By increasing the number of turns of the coil (N)
2. By increasing the magnetic field strength (B), since \[\Phi =BA\], where B is the magnetic field strength and A is the area of the loop.
3. By increasing the speed of movement of the coil or magnet. So the time period will be minimum.
Power transformers, induction cookers and some of the musical instruments are some applications of Faraday’s law.
Note: The minus sign in Faraday's law indicates that the current (I) developed due to the induced emf and magnetic field B are opposing the change in flux. This is known as Lenz law. Faraday’s law suggests that the number of turns, time and change in magnetic flux determines the induced emf quantity.