Question

A square coil of side $25cm$ having $1000$ turns is rotated with an uniform speed in a magnetic field about an axis perpendicular to the direction of the field. At an instant $t$, the emf induced in the coil is $e=200\sin 100\pi t$. The magnetic induction is

• A. $0.50T$
• B. $0.02T$
• C. ${10}^{-3}T$
• D. $0.1T$
• E. $0.01T$

Answer 1

The correct option is E

$0.01T$

Step 1: Given data

Side, $s=25cm$

No. of turns, $N=1000$

Angular frequency, $\omega =100\pi$

E.m.f, $e=200\sin 100\pi t$

Step 2: Find magnetic induction

The standard e.m.f equation is,

$e=NBA\omega Sin\omega t$

Where,

$N=$ no. of turns

$B=$ magnetic field

$A=$ area

$\omega =$ angular frequency

On comparing the given e.m.f with standard e.m.f, we get

$$\begin{gathered} NBA100\pi =200 \\ 1000xBx25x25x100\pi =200 \\ Bx625x\pi =20 \\ B=0.01T \end{gathered}$$

Hence, option E is correct.