A Coil rotates 25 turns about its vertical diameter with angular speed 40 `s ^(-1)` in a horizontal uniform magnetic field of 0.05 T. The coil is of area `300 cm^(2).` Maximum emf is:

Options

A. `0.5 V`
B. `10 V`
C. `1.5 V`
D. `2 V`

Explanation

To find the maximum induced emf in a rotating coil, we can use the formula for the induced emf (ε) in a coil rotating in a magnetic field:

\[ \epsilon = n \cdot B \cdot A \cdot \omega \]

Where:
- \( \epsilon \) = maximum induced emf (in volts)
- \( n \) = number of turns in the coil
- \( B \) = magnetic field strength (in tesla)
- \( A \) = area of the coil (in square meters)
- \( \omega \) = angular speed (in radians per second)

### Step 1: Identify the given values
- Number of turns, \( n = 25 \)
- Magnetic field strength, \( B = 0.05 \, T \)
- Area of the coil, \( A = 300 \, cm^2 = 300 \times 10^{-4} \, m^2 = 0.03 \, m^2 \)
- Angular speed, \( \omega = 40 \, s^{-1} \)

### Step 2: Substitute the values into the formula
Now, we substitute the known values into the formula for induced emf:

\[ \epsilon = 25 \cdot 0.05 \cdot 0.03 \cdot 40 \]

### Step 3: Calculate the induced emf
Now, we perform the multiplication step by step:

1. Calculate \( 25 \cdot 0.05 = 1.25 \)
2. Calculate \( 1.25 \cdot 0.03 = 0.0375 \)
3. Finally, calculate \( 0.0375 \cdot 40 = 1.5 \)

Thus, the maximum induced emf is:

\[ \epsilon = 1.5 \, V \]

### Final Answer
The maximum induced emf is **1.5 volts**.

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