A 70 turn coil with average diameter of 0.02 m is placed perpendicular to magnetic field of 9000 T. If the magnetic field is changed to 6000 T is 3s, what is the magnitude of induced emf ?

Answer

To solve the problem, we will use Faraday's law of electromagnetic induction, which states that the induced electromotive force (emf) in a coil is equal to the negative rate of change of magnetic flux through the coil. The formula for induced emf (ε) is given by:

\[ \epsilon = -N \frac{\Delta \Phi}{\Delta t} \]

Where:
- \(N\) = number of turns in the coil
- \(\Delta \Phi\) = change in magnetic flux
- \(\Delta t\) = change in time

### Step 1: Calculate the area of the coil
The area \(A\) of the coil can be calculated using the formula for the area of a circle:

\[ A = \pi r^2 \]

Where \(r\) is the radius of the coil. Given the diameter is 0.02 m, the radius \(r\) is:

\[ r = \frac{0.02}{2} = 0.01 \, \text{m} \]

Now, substituting the radius into the area formula:

\[ A = \pi (0.01)^2 = \pi \times 0.0001 = 3.14 \times 10^{-4} \, \text{m}^2 \]

### Step 2: Calculate the initial and final magnetic flux
The magnetic flux \(\Phi\) is given by:

\[ \Phi = B \cdot A \]

Where \(B\) is the magnetic field.

1. **Initial magnetic flux (\(\Phi_1\))** with \(B_1 = 9000 \, \text{T}\):

\[ \Phi_1 = B_1 \cdot A = 9000 \cdot 3.14 \times 10^{-4} = 2.826 \, \text{Wb} \]

2. **Final magnetic flux (\(\Phi_2\))** with \(B_2 = 6000 \, \text{T}\):

\[ \Phi_2 = B_2 \cdot A = 6000 \cdot 3.14 \times 10^{-4} = 1.884 \, \text{Wb} \]

### Step 3: Calculate the change in magnetic flux
The change in magnetic flux \(\Delta \Phi\) is:

\[ \Delta \Phi = \Phi_2 - \Phi_1 = 1.884 - 2.826 = -0.942 \, \text{Wb} \]

### Step 4: Calculate the induced emf
Now, we can substitute the values into the induced emf formula:

\[ \epsilon = -N \frac{\Delta \Phi}{\Delta t} \]

Where:
- \(N = 70\) (number of turns)
- \(\Delta t = 3 \, \text{s}\)

Substituting the values:

\[ \epsilon = -70 \cdot \frac{-0.942}{3} = 70 \cdot 0.314 = 22.98 \, \text{V} \]

### Final Answer
The magnitude of the induced emf is approximately:

\[ \epsilon \approx 22.98 \, \text{V} \]