A rectangular coil of dimensions 4 cm x 5 cm with number of turns 20 is placed with its plane perpendicular to a uniform magnetic field of 5 T. If it is moved with a speed of 2 m/s in the field parallel to its length, the e.m.f induced is

Options

A. 0.4V
B. 0.5V
C. 0
D. 0.1V

Answer

To solve the problem of finding the induced electromotive force (e.m.f) in the given rectangular coil, we can follow these steps:

### Step 1: Identify the Given Values
- Dimensions of the rectangular coil: 4 cm x 5 cm
- Number of turns (n): 20
- Magnetic field (B): 5 T (Tesla)
- Speed of the coil (v): 2 m/s

### Step 2: Convert Dimensions to Meters
Since the dimensions are given in centimeters, we need to convert them to meters for consistency in SI units.
- Length (L) = 4 cm = 0.04 m
- Width (W) = 5 cm = 0.05 m

### Step 3: Calculate the Area of the Coil
The area (A) of the rectangular coil can be calculated using the formula:
\[ A = L \times W \]
\[ A = 0.04 \, \text{m} \times 0.05 \, \text{m} = 0.002 \, \text{m}^2 \]

### Step 4: Determine the Angle (θ)
The problem states that the coil is moved parallel to its length in a magnetic field that is perpendicular to the plane of the coil. Therefore, the angle (θ) between the magnetic field and the direction of motion of the coil is:
\[ θ = 0^\circ \]
Thus, \( \sin(θ) = \sin(0^\circ) = 0 \).

### Step 5: Use the Formula for Induced E.M.F
The formula for the induced e.m.f (E) in a moving coil in a magnetic field is given by:
\[ E = n \cdot B \cdot L \cdot v \cdot \sin(θ) \]
Where:
- n = number of turns
- B = magnetic field strength
- L = length of the coil in the direction of motion
- v = speed of the coil
- \( \sin(θ) \) = sine of the angle between the magnetic field and the direction of motion

### Step 6: Substitute the Values
Substituting the known values into the equation:
\[ E = 20 \cdot 5 \cdot 0.04 \cdot 2 \cdot \sin(0^\circ) \]
\[ E = 20 \cdot 5 \cdot 0.04 \cdot 2 \cdot 0 \]
\[ E = 0 \]

### Conclusion
The induced e.m.f in the coil is 0 volts.