Question

Magnetic flux $\left(\varphi \right)$ linked through the coil changes with respect to time $\left(t\right)$ according to following graph, then induced emf $\left(e\right)$ v/s time$\left(t\right)$ graph for coil is:

• A.
• B.
• C.
• D.

Answer 1

The correct option is D

For the magnetic flux $\left(\varphi \right)$ vs time $\left(t\right)$ graph, the slope of the graph is equal to $\frac{d\varphi }{dt}$.

We know that the emf induced in a coil is given by,

$E=-N\frac{d\varphi }{dt}$

For the portion $\text{OA}$:

The magnetic flux increases with time at a constant rate.

$\therefore \frac{d\varphi }{dt}>0$

So, the induced emf will be negative and is constant with time i.e. $e=-ve$.

For portion $\text{AB}$:

$\frac{d\varphi }{dt}=0$ as the magnetic flux is
Constant.

So, the induced emf will be zero i.e. $e=0$

For portion $\text{BC}$:

The magnetic flux decreases with time at constant rate.

$\therefore \frac{d\varphi }{dt}<0$

So, the induced emf is positive and is constant with time i.e. $e=+ve$

Combining all the three results, the graph depicting the variation of the induced emf with time is shown below:




Hence, option ($C$) is the correct answer.

Why this question? Note: According to Faraday's law, $|E|=N\frac{d\varphi }{dt}$ $N$ times the slope of $\varphi -t$ graph gives us the induced e.m.f