Question

A copper disc of radius 0.1 m rotates about an axis passing through its center and perpendicular to its plane with 10 revolutions per second in a uniform transverse magnetic field of 0.1 T. The emf induced across the radius of the disc is:

• A. π/10 V
• B. 2π/10 V
• C. 10 π mV
• D. 20 π mV

Answer 1

The Correct Option is C

To solve the problem, we need to calculate the EMF induced across the radius of a rotating copper disc in a transverse magnetic field.

1. Understanding the Concept:
The EMF induced across the radius of a rotating disc in a uniform magnetic field is given by the formula:
$E = \frac{1}{2} B \omega R^2$
Where:
- $B$ is the magnetic field strength,
- $\omega$ is the angular velocity in radians per second,
- $R$ is the radius of the disc.

2. Given Values:
- $B = 0.1 \, T$
- $R = 0.1 \, m$
- Revolutions per second = 10
- So, angular velocity: $\omega = 2\pi \cdot 10 = 20\pi \, \text{rad/s}$

3. Substituting into the Formula:
$E = \frac{1}{2} \cdot 0.1 \cdot 20\pi \cdot (0.1)^2$
$E = 0.05 \cdot 20\pi \cdot 0.01$
$E = 0.05 \cdot 0.2\pi = 0.01\pi \, \text{V}$

4. Converting to millivolts:
$E = 0.01\pi \cdot 1000 = 10\pi \, \text{mV}$

Final Answer:
The EMF induced across the radius of the disc is $10\pi$ mV.