A magnetic field of flux density 10 T act normal to a 50 turn coil of `100 cm^(2)` area. Find the emf induced in it if the coil is removed from the field in 1/20 s.

Answer

To solve the problem of finding the induced EMF when a coil is removed from a magnetic field, we can follow these steps:

### Step 1: Identify the given values
- Magnetic flux density (B) = 10 T (Tesla)
- Number of turns in the coil (N) = 50 turns
- Area of the coil (A) = 100 cm² = 100 × 10⁻⁴ m² = 0.01 m² (conversion from cm² to m²)
- Time taken to remove the coil from the field (Δt) = 1/20 s = 0.05 s

### Step 2: Calculate the initial magnetic flux (Φ₁)
The magnetic flux (Φ) through the coil is given by the formula:
\[ Φ = B \cdot A \cdot \cos(θ) \]
Since the magnetic field acts normal to the coil, θ = 0° and cos(0°) = 1. Thus,
\[ Φ₁ = B \cdot A = 10 \, \text{T} \cdot 0.01 \, \text{m}² = 0.1 \, \text{Wb} \, (\text{Weber}) \]

### Step 3: Calculate the final magnetic flux (Φ₂)
When the coil is removed from the magnetic field, the magnetic flux becomes zero:
\[ Φ₂ = 0 \, \text{Wb} \]

### Step 4: Calculate the change in magnetic flux (ΔΦ)
The change in magnetic flux (ΔΦ) is given by:
\[ ΔΦ = Φ₂ - Φ₁ = 0 - 0.1 = -0.1 \, \text{Wb} \]

### Step 5: Calculate the induced EMF (E)
The induced EMF can be calculated using Faraday's law of electromagnetic induction:
\[ E = -\frac{ΔΦ}{Δt} \]
Substituting the values:
\[ E = -\frac{-0.1 \, \text{Wb}}{0.05 \, \text{s}} = \frac{0.1}{0.05} = 2 \, \text{V} \]

### Step 6: Calculate the total induced EMF considering the number of turns
Since the coil has 50 turns, the total induced EMF (E_total) is:
\[ E_{total} = N \cdot E = 50 \cdot 2 \, \text{V} = 100 \, \text{V} \]

### Final Answer
The induced EMF in the coil is **100 V**.

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