Which of the following statements is not correct for electromagnetic induction?

The correct statement that is not correct (and therefore the correct answer to the question) is:
"The magnitude of induced emf in a circuit is equal to the total change of magnetic flux through the circuit."

Let us analyze the principles of electromagnetic induction step-by-step to understand why this statement is incorrect while the others are correct:

1. Faraday's Law of Electromagnetic Induction:
According to Faraday's law, the magnitude of the induced electromotive force (emf) in a circuit is directly proportional to the time rate of change of magnetic flux through the circuit, not just the total change in flux.

Mathematically, the induced emf (represented by $\epsilon$) is given by:

$\epsilon =-\frac{d{\Phi }_B}{dt}$

where ${\Phi }_B$ is the magnetic flux and $t$ is time. This confirms that the magnitude depends on how rapidly the flux changes over time ($\frac{d{\Phi }_B}{dt}$), rather than the total net change in flux ($\Delta {\Phi }_B$) alone. Therefore, the statement claiming it is equal to the "total change of magnetic flux" is incorrect.

2. Effect of Number of Turns:
For a closely wound coil containing $N$ turns, the magnetic flux through each turn is the same. The total induced emf is the sum of the emfs induced in each individual turn. Thus, the total induced emf is given by:

$\epsilon =-N\frac{d{\Phi }_B}{dt}$

This shows that increasing the number of turns $N$ directly increases the magnitude of the induced emf.

3. Lenz's Law:
The negative sign in Faraday's law represents Lenz's Law. It states that the polarity of the induced emf is such that it generates an electric current whose magnetic field opposes the change in magnetic flux that produced it.