The flux associated with coil changes from 1.35 Wb to 0.79 Wb within `(1)/(10)`s. then, the charge produced by the earth coil, if resistance of coil is `7Omega` is

Options

A. 0.08 C
B. 0.8 C
C. 0.008C
D. 8C

Answer

To solve the problem step by step, we will follow the principles of electromagnetic induction and Ohm's law.

### Step 1: Identify the given values
- Initial magnetic flux, \( \Phi_1 = 1.35 \, \text{Wb} \)
- Final magnetic flux, \( \Phi_2 = 0.79 \, \text{Wb} \)
- Time interval, \( t = \frac{1}{10} \, \text{s} = 0.1 \, \text{s} \)
- Resistance of the coil, \( R = 7 \, \Omega \)

### Step 2: Calculate the change in magnetic flux
The change in magnetic flux \( \Delta \Phi \) can be calculated as:
\[ \Delta \Phi = \Phi_1 - \Phi_2 = 1.35 \, \text{Wb} - 0.79 \, \text{Wb} = 0.56 \, \text{Wb} \]

### Step 3: Calculate the induced EMF (Electromotive Force)
According to Faraday's law of electromagnetic induction, the induced EMF \( \mathcal{E} \) is given by the rate of change of magnetic flux:
\[ \mathcal{E} = -\frac{d\Phi}{dt} \]
Substituting the values:
\[ \mathcal{E} = -\frac{0.56 \, \text{Wb}}{0.1 \, \text{s}} = -5.6 \, \text{V} \]
(Note: The negative sign indicates the direction of the induced EMF, but we will use the magnitude for calculations.)

### Step 4: Calculate the current using Ohm's Law
Using Ohm's law, the current \( I \) can be calculated as:
\[ I = \frac{\mathcal{E}}{R} \]
Substituting the values:
\[ I = \frac{5.6 \, \text{V}}{7 \, \Omega} = 0.8 \, \text{A} \]

### Step 5: Calculate the charge produced
The charge \( Q \) produced can be calculated using the relationship between charge, current, and time:
\[ Q = I \cdot t \]
Substituting the values:
\[ Q = 0.8 \, \text{A} \times 0.1 \, \text{s} = 0.08 \, \text{C} \]

### Final Answer
The charge produced by the coil is \( Q = 0.08 \, \text{C} \).

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