A coil of area `2m^2` and resistane `4Omega` is placed perpendicular to a uniform magnetic field of `4T`. The loop is rotated by `90^@` in `0.1` second. Choose the correct options.

Options

A. average induced emf in the coil is `8V`
B. average induced current in the circuit is `20A`
C. `2C `charge wil flow i the coil in above period
D. Heat produced in the coil in the above period can't be determined from the given datas

Explanation

To solve the problem step by step, we will calculate the initial magnetic flux, the final magnetic flux after the coil is rotated, the change in magnetic flux, the induced electromotive force (emf), the induced current, and the charge flown through the coil.

### Step 1: Calculate the Initial Magnetic Flux
The initial magnetic flux (Φ_initial) when the coil is perpendicular to the magnetic field is given by the formula:
\[ \Phi_{\text{initial}} = B \cdot A \cdot \cos(\theta) \]
where:
- \(B = 4 \, \text{T}\) (magnetic field strength)
- \(A = 2 \, \text{m}^2\) (area of the coil)
- \(\theta = 0^\circ\) (angle between the magnetic field and the normal to the coil)

Calculating:
\[ \Phi_{\text{initial}} = 4 \cdot 2 \cdot \cos(0) = 4 \cdot 2 \cdot 1 = 8 \, \text{Wb} \]

### Step 2: Calculate the Final Magnetic Flux
After the coil is rotated by \(90^\circ\), the angle becomes \(90^\circ\):
\[ \Phi_{\text{final}} = B \cdot A \cdot \cos(90^\circ) = 4 \cdot 2 \cdot 0 = 0 \, \text{Wb} \]

### Step 3: Calculate the Change in Magnetic Flux
The change in magnetic flux (\(\Delta \Phi\)) is given by:
\[ \Delta \Phi = \Phi_{\text{final}} - \Phi_{\text{initial}} = 0 - 8 = -8 \, \text{Wb} \]

### Step 4: Calculate the Induced EMF
The induced emf (\(E\)) can be calculated using Faraday's law of electromagnetic induction:
\[ E = -\frac{\Delta \Phi}{\Delta t} \]
where \(\Delta t = 0.1 \, \text{s}\):
\[ E = -\frac{-8}{0.1} = \frac{8}{0.1} = 80 \, \text{V} \]

### Step 5: Calculate the Induced Current
Using Ohm's law, the induced current (\(I\)) can be calculated as:
\[ I = \frac{E}{R} \]
where \(R = 4 \, \Omega\):
\[ I = \frac{80}{4} = 20 \, \text{A} \]

### Step 6: Calculate the Charge Flown
The charge (\(Q\)) that flows through the coil can be calculated using:
\[ Q = \frac{\Delta \Phi}{R} \]
Substituting the values:
\[ Q = \frac{8}{4} = 2 \, \text{C} \]

### Summary of Results
- Induced EMF: \(80 \, \text{V}\)
- Induced Current: \(20 \, \text{A}\)
- Charge Flown: \(2 \, \text{C}\)