Question

In a coil of resistance of $10\Omega$, the induced current $i$ developed by changing magnetic flux through it, is shown in the figure as a function of time. The magnitude of changing flux through the coil in $\text{Wb}$ is

• A. $8$
• B. $4$
• C. $2$
• D. $6$

Answer 1

The correct option is C $2$

When a coil is placed in a magnetic field, then an $emf$ is induced in that loop and some charge $q$ will flow through the coil which is given by

$\Rightarrow q=\left|\frac{-\Delta \varphi }{R}\right|$

$\Rightarrow \Delta \varphi =qR....\left(1\right)$

As current, $i=\frac{dq}{dt}$

$\Rightarrow \int dq=\int idt$

$q=\int idt=$ Area under the $i-t$ graph

$\therefore q=\frac{1}{2}\times 0.1\times 4=0.2\text{C}$

Using equation $\left(1\right)$,

$\Rightarrow \Delta \varphi =0.2\times 10=2\text{Wb}$

Hence, option $\left(C\right)$ is correct answer.