Question

A metal disc of radius $100cm$ is rotated at a constant angular speed of $60rad{s}^{-1}$ in a plane at right angles to an external field of magnetic induction $0.05Wb{m}^{-2}$. The e.m.f induced between the center and a point on the rim will be

• A. $3V$
• B. $1.5V$
• C. $6V$
• D. $9V$

Answer 1

The correct option is B

$1.5V$

Step 1. Given data:

The radius of the metal disc, $R=100cm$$=1m$

Angular speed, $\omega =60rad/s$

Magnetic induction, $B=0.05Wb/m^2$

Step 2. Calculating induced EMF

Induced EMF produced between the center and a point on the disc is given by,

$e=\frac{1}{2}\times \omega \times B\times R^2$ [$e$is EMF]

$$\begin{gathered} \Rightarrow e=\frac{1}{2}\times 60\times 0.05\times {\left(1\right)}^2 \\ \therefore e=1.5V \end{gathered}$$

Hence, the correct option is ($B$).