A rectangular coil of resistance 10 `Omega` has 2000 turns. Find the emf induced in the coil if the magnetic flux through it changes from `6 xx 10^(-4)` Wb to `2 xx 10^(-4)` Wb in 0.1 second. Also calculate the current flowing through it.

Answer

To solve the problem, we will follow these steps:

### Step 1: Identify the given values
- Resistance of the coil (R) = 10 Ω
- Number of turns (N) = 2000 turns
- Initial magnetic flux (Φ1) = \(6 \times 10^{-4}\) Wb
- Final magnetic flux (Φ2) = \(2 \times 10^{-4}\) Wb
- Time interval (Δt) = 0.1 s

### Step 2: Calculate the change in magnetic flux (ΔΦ)
The change in magnetic flux can be calculated using the formula:
\[ \Delta \Phi = \Phi_2 - \Phi_1 \]
Substituting the values:
\[ \Delta \Phi = (2 \times 10^{-4}) - (6 \times 10^{-4}) = -4 \times 10^{-4} \text{ Wb} \]

### Step 3: Calculate the induced emf (ε)
The induced emf can be calculated using Faraday's law of electromagnetic induction:
\[ \text{Induced emf} (\epsilon) = -N \frac{\Delta \Phi}{\Delta t} \]
Substituting the values:
\[ \epsilon = -2000 \times \frac{-4 \times 10^{-4}}{0.1} \]
Calculating the right-hand side:
\[ \epsilon = 2000 \times \frac{4 \times 10^{-4}}{0.1} = 2000 \times 4 \times 10^{-3} = 8 \text{ V} \]

### Step 4: Calculate the current (I)
Using Ohm's law, the current can be calculated as:
\[ I = \frac{\epsilon}{R} \]
Substituting the values:
\[ I = \frac{8}{10} = 0.8 \text{ A} \]

### Final Answers
- Induced emf = 8 V
- Current flowing through the coil = 0.8 A

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