Question 36: Electromagnetic Induction

Question

A circular loop of radius 7 cm is placed in uniform magnetic field of 0.2 T directed perpendicular to plane of loop. The loop is converted into a square loop in 0.5 s . The EMF induced in the loop is $\_\_\_\_$ mV.

Accepted Answer

According to Faraday's Law of Electromagnetic Induction, the induced EMF (E) is equal to the rate of change of magnetic flux $(\phi)$ through the loop.
Initially circular loop is with radius $\mathrm{r}=7 \mathrm{~cm}=0.07 \mathrm{~m}$.
Finally a square loop formed from the same wire.
Magnetic field $\mathrm{B}=0.2 \mathrm{~T}$ (constant and perpendicular).
Time interval $=\Delta \mathrm{t}=0.5 \mathrm{~s}$.
Initial Area ( $\mathrm{A}_1$ )
$$ \mathrm{A}_1=\pi \mathrm{r}^2=\pi 	imes(0.07)^2=0.0154 \mathrm{~m}^2 $$
The perimeter of the square must be equal to the circumference of the circle because the wire length is constant.
$$ 2 \pi \mathrm{r}=4 \mathrm{a} \Rightarrow \mathrm{a}=\frac{2 \pi \mathrm{r}}{4}=\frac{\pi \mathrm{r}}{2}=\frac{\pi 	imes 0.07}{2} \mathrm{~m}=0.11 \mathrm{~m} $$
So, final area ( $\mathrm{A}_2$ )
$$ a^2=(0.11)^2=0.0121 m^2 . $$
Since the field is perpendicular, $\phi=\mathrm{B} \cdot \mathrm{A}$.
So, the change in magnetic flux is,
$$ \Delta \phi=\mathrm{B}\left(\mathrm{~A}_2-\mathrm{A}_1ight) $$
$$\Rightarrow $$ $\Delta \phi=0.2 	imes(0.0121-0.0154)$
$$\Rightarrow $$ $\Delta \phi=0.2 	imes(-0.0033)=-0.00066 \mathrm{~Wb}$
The magnitude of the induced EMF is :
$$ |E|=\left|\frac{\Delta \phi}{\Delta t}ight| $$
$$\Rightarrow $$ $$ |\mathrm{E}|=\frac{0.00066}{0.5}=0.00132 \mathrm{~V}=0.00132 	imes 1000 \mathrm{mV}=1.32 \mathrm{mV} $$
Therefore, the induced EMF is 1.32 mV .
Hence, the correct option is (C).

Answer

13.2

Answer

6.6

Answer

1.32

Answer

8.25

Electromagnetic Induction

A circular loop of radius 7 cm is placed in uniform magnetic field of 0.2 T directed perpendicular to plane of loop. The loop is converted into a square loop in 0.5 s . The EMF induced in the loop is \_\_\_\_ mV.

Choose the correct answer: