If the magnetic field is parallel to a surface then, the magnetic flux through the surface is

Options

A. zero
B. small but not zero
C. infinite
D. large but not infinite

Answer

To solve the problem, we need to understand the concept of magnetic flux and how it relates to the orientation of the magnetic field with respect to a surface.

### Step-by-Step Solution:

1. **Understanding Magnetic Flux**:
Magnetic flux (Φ) through a surface is defined as the product of the magnetic field (B) and the area (A) of the surface, taking into account the angle (θ) between the magnetic field and the normal (perpendicular) to the surface. The formula for magnetic flux is given by:
\[ \Phi = B \cdot A \cdot \cos(\theta) \]

2. **Identifying the Angle**:
In this scenario, the magnetic field is parallel to the surface. This means that the angle (θ) between the magnetic field and the normal to the surface is 90 degrees (90°).

3. **Calculating the Cosine of the Angle**:
We know that:
\[ \cos(90°) = 0 \]

4. **Substituting Values into the Flux Formula**:
Now, substituting the angle into the magnetic flux formula:
\[ \Phi = B \cdot A \cdot \cos(90°) = B \cdot A \cdot 0 \]

5. **Conclusion**:
Therefore, the magnetic flux through the surface is:
\[ \Phi = 0 \]

### Final Answer:
If the magnetic field is parallel to a surface, then the magnetic flux through the surface is **0**.

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