A 100 turns coil of area of cross section `200 cm^(2)` having `2 Omega` resistance is held perpendicular to a magnetic field of 0.1 T. If it is removed from the magnetic field in one second, the induced charge produced in it is

Options

A. 0.2 C
B. 2C
C. 0.1C
D. 1C

Explanation

To solve the problem, we need to calculate the induced charge produced in a coil when it is removed from a magnetic field. We will follow these steps:

### Step 1: Calculate the change in magnetic flux (ΔΦ)
The magnetic flux (Φ) through a coil is given by the formula:
\[ \Phi = B \cdot A \cdot \cos(\theta) \]
Where:
- \(B\) is the magnetic field strength (0.1 T),
- \(A\) is the area of the coil,
- \(\theta\) is the angle between the magnetic field and the normal to the coil's surface (90 degrees here, so \(\cos(90^\circ) = 1\)).

Given:
- The area \(A = 200 \, \text{cm}^2 = 200 \times 10^{-4} \, \text{m}^2 = 0.02 \, \text{m}^2\).

Now, the initial magnetic flux when the coil is in the magnetic field is:
\[ \Phi_{\text{initial}} = B \cdot A = 0.1 \, \text{T} \cdot 0.02 \, \text{m}^2 = 0.002 \, \text{Wb} \]

When the coil is removed from the magnetic field, the final magnetic flux is:
\[ \Phi_{\text{final}} = 0 \, \text{Wb} \]

Thus, the change in magnetic flux (ΔΦ) is:
\[ \Delta \Phi = \Phi_{\text{final}} - \Phi_{\text{initial}} = 0 - 0.002 = -0.002 \, \text{Wb} \]

### Step 2: Calculate the induced EMF (E)
According to Faraday's law of electromagnetic induction, the induced EMF (E) is given by:
\[ E = -\frac{d\Phi}{dt} \]
For a coil with \(N\) turns, the induced EMF is:
\[ E = -N \cdot \frac{\Delta \Phi}{\Delta t} \]
Where:
- \(N = 100\) (number of turns),
- \(\Delta t = 1 \, \text{s}\).

Substituting the values:
\[ E = -100 \cdot \frac{-0.002}{1} = 0.2 \, \text{V} \]

### Step 3: Calculate the current (I)
Using Ohm's law, the current (I) can be calculated as:
\[ I = \frac{E}{R} \]
Where \(R = 2 \, \Omega\) (resistance of the coil).

Substituting the values:
\[ I = \frac{0.2}{2} = 0.1 \, \text{A} \]

### Step 4: Calculate the induced charge (Q)
The induced charge (Q) can be calculated using the formula:
\[ Q = I \cdot t \]
Where \(t = 1 \, \text{s}\).

Substituting the values:
\[ Q = 0.1 \, \text{A} \cdot 1 \, \text{s} = 0.1 \, \text{C} \]

### Final Answer
The induced charge produced in the coil is \(0.1 \, \text{C}\).

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