A copper disk of radius 0.1m is rotated about its center with 200 rev/s in uniform magnetic field. Induced emf across the radius of the disc is:

Options

A. `(pi)/(20)V`
B. `(pi)/(100)V`
C. `20pi mV`
D. 0

Explanation

To find the induced EMF across the radius of a rotating copper disk in a uniform magnetic field, we can use the formula for induced EMF in a rotating conductor. Here's a step-by-step solution:

### Step 1: Understand the parameters
- **Radius of the disk (r)** = 0.1 m
- **Revolutions per second (n)** = 200 rev/s
- **Angular velocity (ω)** = 2πn = 2π × 200 rad/s

### Step 2: Calculate the angular velocity (ω)
Using the formula for angular velocity:
\[ \omega = 2\pi n \]
Substituting the value of n:
\[ \omega = 2\pi \times 200 = 400\pi \, \text{rad/s} \]

### Step 3: Determine the induced EMF (ε)
The induced EMF (ε) across the radius of the disk can be calculated using the formula:
\[ \epsilon = \frac{1}{2} B \omega r^2 \]
where B is the magnetic field strength (which is not given in the problem). However, we can express the EMF in terms of B.

### Step 4: Substitute the values into the EMF formula
Substituting the values we have:
\[ \epsilon = \frac{1}{2} B (400\pi) (0.1)^2 \]
\[ \epsilon = \frac{1}{2} B (400\pi) (0.01) \]
\[ \epsilon = 2B\pi \, \text{V} \]

### Final Result
The induced EMF across the radius of the disk is:
\[ \epsilon = 2B\pi \, \text{V} \]
where B is the magnetic field strength.