A coil is placed in a magnetic field directed downward and increasing from 0 to 18 T in 0.1 s. area of coil is 2 `m^(2)` and resistance 5 `Omega`. Induced current will be

Options

A. 72 A anticlockwise direction
B. 27 A anticlockwise direction
C. 72 A clockwise direction
D. 27 A clockwise direction

Explanation

To find the induced current in the coil placed in a changing magnetic field, we can follow these steps:

### Step 1: Calculate the Change in Magnetic Flux
The magnetic flux (Φ) through the coil is given by the formula:
\[ \Phi = B \cdot A \]
Where:
- \(B\) is the magnetic field strength (in Tesla)
- \(A\) is the area of the coil (in square meters)

Given:
- Initial magnetic field \(B_i = 0 \, T\)
- Final magnetic field \(B_f = 18 \, T\)
- Area \(A = 2 \, m^2\)

The change in magnetic flux (\(\Delta \Phi\)) is:
\[ \Delta \Phi = \Phi_f - \Phi_i = (B_f \cdot A) - (B_i \cdot A) = (18 \, T \cdot 2 \, m^2) - (0 \, T \cdot 2 \, m^2) = 36 \, Wb \]

### Step 2: Calculate the Induced EMF
According to Faraday's law of electromagnetic induction, the induced EMF (\(E\)) is given by:
\[ E = -\frac{d\Phi}{dt} \]
Since the change in flux occurs over a time interval (\(dt\)), we can express it as:
\[ E = -\frac{\Delta \Phi}{\Delta t} \]
Given that \(\Delta t = 0.1 \, s\):
\[ E = -\frac{36 \, Wb}{0.1 \, s} = -360 \, V \]
(The negative sign indicates the direction of the induced EMF according to Lenz's law, but we will consider the magnitude for current calculation.)

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

Given:
- \(R = 5 \, \Omega\)

Substituting the values:
\[ I = \frac{360 \, V}{5 \, \Omega} = 72 \, A \]

### Step 4: Determine the Direction of the Induced Current
According to Lenz's law, the direction of the induced current will be such that it opposes the change in magnetic flux. Since the magnetic field is increasing downwards, the induced current will flow in a direction that creates a magnetic field opposing this increase. Therefore, the induced current will flow in an anticlockwise direction when viewed from above.

### Final Answer
The induced current in the coil is **72 A** and flows in an **anticlockwise direction**.

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