The magnetic field perpendicular to the plane of a loop of area `7m^(2)` is 13T. Find the magnetic flux of the loop?

Options

A. 12 Wb
B. 12 Wb
C. 91 Wb
D. 554 Wb

Explanation

To find the magnetic flux through a loop when the magnetic field is perpendicular to the plane of the loop, we can use the formula for magnetic flux (Φ):

\[ \Phi = B \cdot A \cdot \cos(\theta) \]

Where:
- \( \Phi \) is the magnetic flux,
- \( B \) is the magnetic field strength,
- \( A \) is the area of the loop,
- \( \theta \) is the angle between the magnetic field and the normal (perpendicular) to the surface of the loop.

### Step-by-Step Solution:

1. **Identify the Given Values**:
- Area of the loop, \( A = 7 \, m^2 \)
- Magnetic field strength, \( B = 13 \, T \)
- Since the magnetic field is perpendicular to the plane of the loop, the angle \( \theta = 0^\circ \).

2. **Calculate Cosine of the Angle**:
- \( \cos(0^\circ) = 1 \)

3. **Substitute the Values into the Formula**:
- Now, we can substitute the values into the magnetic flux formula:
\[ \Phi = B \cdot A \cdot \cos(\theta) = 13 \, T \cdot 7 \, m^2 \cdot 1 \]

4. **Perform the Multiplication**:
- Calculate \( 13 \cdot 7 \):
\[ 13 \cdot 7 = 91 \]

5. **Final Result**:
- Therefore, the magnetic flux \( \Phi = 91 \, Wb \) (Weber).

### Conclusion:
The magnetic flux through the loop is \( 91 \, Wb \).

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