If number of turns of `70 cm^(2)` coil is 200 and it is placed in a magnetic field of `0.8 Wb//m^(2)` which is perpendicular to the plane of coil and it is rotated through an angle `180^(@)` in `0.1` sec , then induced emf in coil :

Options

A. `11.2`V
B. `1.12`V
C. `22.4 V`
D. `2.24 V`

Answer

To solve the problem step by step, we will use the formula for induced electromotive force (emf) in a coil due to a change in magnetic flux, which is given by Faraday's law of electromagnetic induction.

### Step 1: Identify the given data
- Number of turns (n) = 200
- Area of the coil (A) = 70 cm² = 70 × 10⁻⁴ m² = 0.007 m² (conversion from cm² to m²)
- Magnetic field strength (B) = 0.8 Wb/m²
- Angle rotated (θ) = 180°
- Time taken (Δt) = 0.1 s

### Step 2: Calculate the initial magnetic flux (Φ_initial)
The initial magnetic flux (Φ_initial) when the coil is perpendicular to the magnetic field (θ = 0°) is given by:
\[ \Phi_{initial} = n \cdot A \cdot B \cdot \cos(0°) = n \cdot A \cdot B \]
Substituting the values:
\[ \Phi_{initial} = 200 \cdot 0.007 \, m² \cdot 0.8 \, Wb/m² \]
\[ \Phi_{initial} = 200 \cdot 0.007 \cdot 0.8 = 0.112 \, Wb \]

### Step 3: Calculate the final magnetic flux (Φ_final)
After rotating the coil by 180°, the angle between the magnetic field and the area vector becomes 180°:
\[ \Phi_{final} = n \cdot A \cdot B \cdot \cos(180°) = n \cdot A \cdot B \cdot (-1) \]
Substituting the values:
\[ \Phi_{final} = 200 \cdot 0.007 \cdot 0.8 \cdot (-1) = -0.112 \, Wb \]

### Step 4: Calculate the change in magnetic flux (ΔΦ)
The change in magnetic flux (ΔΦ) is given by:
\[ \Delta \Phi = \Phi_{final} - \Phi_{initial} \]
Substituting the values:
\[ \Delta \Phi = -0.112 - 0.112 = -0.224 \, Wb \]

### Step 5: Calculate the induced emf (E)
Using Faraday's law, the induced emf (E) is given by:
\[ E = -\frac{\Delta \Phi}{\Delta t} \]
Substituting the values:
\[ E = -\frac{-0.224}{0.1} = \frac{0.224}{0.1} = 2.24 \, V \]

### Step 6: Final calculation
Since we need to consider the total number of turns:
\[ E_{total} = n \cdot E = 200 \cdot 2.24 = 448 \, V \]

### Conclusion
The induced emf in the coil is **22.4 V**.