The net magnetic flux through any closed surface, kept in a magnetic field is

Options

A. zero
B. `(mu_(0))/(4pi)`
C. `4pimu_(0)`
D. `(4mu_(0))/(pi)`

Explanation

To solve the question regarding the net magnetic flux through any closed surface kept in a magnetic field, we can follow these steps:

### 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, projected in the direction of the magnetic field. Mathematically, it can be expressed as:
\[ \Phi = \int \mathbf{B} \cdot d\mathbf{A} \]
where \(d\mathbf{A}\) is a differential area vector.

2. **Closed Surface Concept**:
We are considering a closed surface, which means it completely encloses a volume. Examples include spheres, cubes, etc.

3. **Gauss's Law for Magnetism**:
According to Gauss's law for magnetism, the net magnetic flux through any closed surface is zero. This is expressed mathematically as:
\[ \Phi = \oint \mathbf{B} \cdot d\mathbf{A} = 0 \]
This implies that the number of magnetic field lines entering the closed surface is equal to the number of magnetic field lines leaving the surface.

4. **Reasoning**:
Magnetic field lines are continuous and do not begin or end at any point (they are always closed loops). Therefore, any magnetic field line that enters a closed surface must also exit it, resulting in a net flux of zero.

5. **Conclusion**:
Based on the above reasoning, we conclude that the net magnetic flux through any closed surface kept in a magnetic field is zero.

### Final Answer:
The net magnetic flux through any closed surface kept in a magnetic field is **0**.

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