A magnetic flux of 500 microweber passing through a 200 turn coil is reversed in `20xx10^(-3)s`. The average induced emf in the coil (in volt) is

Options

A. 2.5
B. `5.0`
C. 7.5
D. `10.0`

Answer

To solve the problem, we need to calculate the average induced electromotive force (emf) in a coil when the magnetic flux through it is reversed. Here’s the step-by-step solution:

### Step 1: Identify Given Values
- Magnetic flux (Φ_initial) = 500 microweber (µWb) = 500 × 10^(-6) Wb
- Number of turns in the coil (N) = 200 turns
- Time taken for the reversal (Δt) = 20 × 10^(-3) s

### Step 2: Calculate Final Magnetic Flux
Since the magnetic flux is reversed, the final magnetic flux (Φ_final) will be:
- Φ_final = -500 microweber = -500 × 10^(-6) Wb

### Step 3: Calculate Change in Magnetic Flux
The change in magnetic flux (ΔΦ) can be calculated as:
\[ ΔΦ = Φ_final - Φ_initial \]
Substituting the values:
\[ ΔΦ = (-500 × 10^{-6}) - (500 × 10^{-6}) = -1000 × 10^{-6} \text{ Wb} \]
The magnitude of change in magnetic flux is:
\[ |ΔΦ| = 1000 × 10^{-6} \text{ Wb} = 1 × 10^{-3} \text{ Wb} \]

### Step 4: Calculate Average Induced EMF
The average induced emf (ε) in the coil can be calculated using Faraday's law of electromagnetic induction:
\[ ε = -N \frac{ΔΦ}{Δt} \]
Substituting the values:
\[ ε = -200 \times \frac{1 × 10^{-3}}{20 × 10^{-3}} \]

### Step 5: Simplify the Expression
\[ ε = -200 \times \frac{1}{20} = -200 \times 0.05 = -10 \text{ V} \]
The negative sign indicates the direction of the induced emf, but we are interested in the magnitude:
\[ |ε| = 10 \text{ V} \]

### Final Answer
The average induced emf in the coil is **10 volts**.

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