Magnetic flux in a circuite containing a coil of resistance `2Omega`change from `2.0Wb` to `10 Wb` in `0.2 sec`. The charge passed through the coil in this time is

Options

A. 5.0 C
B. 4.0 C
C. 1.0 C
D. 0.8 C

Explanation

To solve the problem, we need to find the charge that passes through a coil when the magnetic flux changes. Here are the steps to arrive at the solution:

### Step 1: Identify the given values
- Initial magnetic flux (\( \Phi_i \)) = 2.0 Wb
- Final magnetic flux (\( \Phi_f \)) = 10.0 Wb
- Resistance of the coil (\( R \)) = 2 Ω
- Time interval (\( t \)) = 0.2 s

### Step 2: Calculate the change in magnetic flux
The change in magnetic flux (\( \Delta \Phi \)) can be calculated as:
\[ \Delta \Phi = \Phi_f - \Phi_i = 10.0 \, \text{Wb} - 2.0 \, \text{Wb} = 8.0 \, \text{Wb} \]

### Step 3: Calculate the induced EMF
According to Faraday's law of electromagnetic induction, the induced electromotive force (EMF) (\( \mathcal{E} \)) is given by the negative rate of change of magnetic flux:
\[ \mathcal{E} = -\frac{\Delta \Phi}{\Delta t} \]
Substituting the values:
\[ \mathcal{E} = -\frac{8.0 \, \text{Wb}}{0.2 \, \text{s}} = -40.0 \, \text{V} \]
(Note: The negative sign indicates the direction of the induced EMF, but we will use the magnitude for further calculations.)

### Step 4: Calculate the induced current
Using Ohm's law, the induced current (\( I \)) can be calculated as:
\[ I = \frac{\mathcal{E}}{R} = \frac{40.0 \, \text{V}}{2 \, \Omega} = 20.0 \, \text{A} \]

### Step 5: Calculate the charge passed through the coil
The charge (\( Q \)) that passes through the coil can be calculated using the formula:
\[ Q = I \times t \]
Substituting the values:
\[ Q = 20.0 \, \text{A} \times 0.2 \, \text{s} = 4.0 \, \text{C} \]

### Final Answer
The charge passed through the coil in this time is \( 4.0 \, \text{C} \).

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