Question

The magnetic field in a coil of $100$turns and $40squarecm$area is increased from $1tesla$ to $6tesla$ in $2$ second. The magnetic field is perpendicular to the coil. The e.m.f. generated in it is

• A. $104V$
• B. $1.2V$
• C. $1.0V$
• D. ${10}^{-2}V$

Answer 1

The correct option is C

$1.0V$

Step 1: Given data:

No of turns of coil $N=100$

The area $A=40c{m}^2$

Time $t=2sec$

The increasing difference$∆B=\left(6-1\right)Tesla$

magnetic field is perpendicular to the coil

Step 2: Formula used:

The emf can be calculated using the formula-

$e=-N\left(\frac{∆B}{t}\right).A\cos \theta$

Where $e$is the e.m.f, $N$ is the number of coils, $∆B$is the difference, and $A$is the area of the coil.

Step 3: Calculation of emf generated:

Therefore substitute the known values in the formula,

Since the magnetic field $(\overrightarrow{B})$ and $(\overrightarrow{A})$ are parallel to each other, therefore $\theta =0$

$$\begin{gathered} e=-100\left(\frac{6-1}{2}\right)\times 40\times \cos 0 \\ e=-100\times 2.5\times 40\times {10}^{-4}\times 1 \\ e=-1 \\ \left|e\right|=1V \end{gathered}$$

Therefore the e.m.f. generated is$1.0V$.

Hence, option C is the correct answer.