A coil is places perpendicular to a magnetic field of "5000T" .When the field is changed to "3000T" in "2s" ,an induced emf of "22V" is produced in the coil.If the diameter of the coil is "0.02m" ,then the number of turns in the coil is:

Options

A. 7
B. 35
C. 140
D. 70

Answer

To find the number of turns in the coil, we will use the formula for induced electromotive force (emf) due to a change in magnetic flux. The formula is given by:

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

Where:
- \(E\) is the induced emf,
- \(N\) is the number of turns in the coil,
- \(\Delta \Phi\) is the change in magnetic flux,
- \(\Delta t\) is the time interval during which the change occurs.

### Step 1: Calculate the change in magnetic field
Given:
- Initial magnetic field, \(B_1 = 5000 \, T\)
- Final magnetic field, \(B_2 = 3000 \, T\)

The change in magnetic field (\(\Delta B\)) is:
\[ \Delta B = B_2 - B_1 = 3000 \, T - 5000 \, T = -2000 \, T \]

### Step 2: Calculate the area of the coil
The diameter of the coil is given as \(0.02 \, m\), so the radius \(r\) is:
\[ r = \frac{0.02}{2} = 0.01 \, m \]

The area \(A\) of the coil is given by the formula for the area of a circle:
\[ A = \pi r^2 = \pi (0.01)^2 = \pi \times 0.0001 \, m^2 = 0.0001\pi \, m^2 \]

### Step 3: Calculate the change in magnetic flux
The change in magnetic flux (\(\Delta \Phi\)) is given by:
\[ \Delta \Phi = A \Delta B = A (B_2 - B_1) = A \times (-2000 \, T) \]
Substituting the area:
\[ \Delta \Phi = (0.0001\pi) \times (-2000) = -0.2\pi \, Wb \]

### Step 4: Substitute values into the induced emf formula
We know the induced emf \(E = 22 \, V\) and the time interval \(\Delta t = 2 \, s\). Now substituting into the induced emf formula:
\[ 22 = N \frac{-0.2\pi}{2} \]

### Step 5: Solve for \(N\)
Rearranging the formula to solve for \(N\):
\[ N = \frac{22 \times 2}{-0.2\pi} = \frac{44}{-0.2\pi} \]
Calculating the value:
\[ N = \frac{44}{-0.2 \times 3.14} \approx \frac{44}{-0.628} \approx -70 \]
Since the number of turns cannot be negative, we take the absolute value:
\[ N \approx 70 \]

### Final Answer
The number of turns in the coil is approximately \(70\).

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