Question

The net magnetic flux through any closed surface is:

• A. Negative
• B. Zero
• C. Positive
• D. Infinity

Answer 1

The Correct Option is B

The given question pertains to the concept of magnetic flux, which is part of Gauss's Law for Magnetism in electromagnetic theory.

The law states that the net magnetic flux \(\Phi_B\) through any closed surface is always zero. This is mathematically expressed as:

\[\oint_S \mathbf{B} \cdot d\mathbf{A} = 0\]

where:

• \(\oint_S\) denotes the closed surface integral over surface S.
• \(\mathbf{B}\) is the magnetic field vector.
• \(\cdot\) indicates the dot product.
• d\mathbf{A} is the differential area vector on the surface.

This principle implies that magnetic monopoles do not exist; hence, the magnetic field lines are always continuous loops. The field lines that enter a closed surface must exit it as well, resulting in a net flux of zero. This explains why the net magnetic field cannot be negative, positive, or infinite through a closed surface.

From the given options:

• Negative
  : Incorrect because magnetic flux cannot have a net negative value through a closed surface.
• Zero
  : Correct as per Gauss's Law for Magnetism.
• Positive
  : Incorrect for similar reasons as negative flux; it cannot be unbalanced across a closed surface.
• Infinity
  : Incorrect since magnetic flux must be finite and zero for a closed surface.

Therefore, the correct answer is Zero.