Question

A $50$turns circular coil has a radius of $3cm$, it is kept in a magnetic field acting normal to the area of the coil. The magnetic field $B$ increased from $0.10tesla$ to $0.35tesla$ in $2milliseconds$. The average induced e.m.f. in the coils is

• A. $1.77volts$
• B. $17.7volts$
• C. $177volts$
• D. $0.177volts$

Answer 1

The correct option is B

$17.7volts$

Step 1: Given data

No. of turns in the coil, $N=50$

Radius of the circular coil, $r=3cm$

$=3\times {10}^{-2}m\left[As1m={10}^{2}cm\right]$

Initial value of magnetic field, $B_1=0.10Tesla$

Final value of magnetic field, $B_2=0.35Tesla$

Time interval, $T=2ms$

$=2\times {10}^{-3}s$

Step 2: Find the magnetic flux, $\mathit{\varphi }$

The initial value of flux, ${\varphi }_1=N{B}_{1}A$

The final value of flux, ${\varphi }_2=N{B}_{2}A$

Step 3: Find the value of induced emf, $e$

Value of induced emf, $e=(N{B}_{1}A–N{B}_{2}A)/t$

$$\begin{gathered} =(NA/t)[B_2–B_1] \\ =\left(N\times \pi \times r^2/t\right)\left[B_2-B_1\right] \\ =\left[50\times 3.14\times {\left(3\times {10}^{-3}\right)}^2\right]\left[0.35-0.10\right] \\ =17.675Volts \\ =17.7V \end{gathered}$$

Hence, option (B) is correct.