16.3: Gauss’s Law for Magnetism
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By analogy with Gauss’s law for the electric field, we could write a Gauss’s law for the magnetic field as follows:
\[\Phi_{B}=C q_{\text{magnetic inside }}\label{16.11}\]
where \(Φ_B\) is the outward magnetic flux through a closed surface, \(C \) is a constant, and \(q_{\text{magnetic inside}}\) is the “magnetic charge” inside the closed surface. Extensive searches have been made for magnetic charge, generally called a magnetic monopole. However, none has ever been found. Thus, Gauss’s law for magnetism can be written
\[\Phi_{B}=0 \quad \text { (Gauss's law for magnetism). }\label{16.12}\]
This of course doesn’t preclude non-zero values of the magnetic flux through open surfaces, as illustrated in figure 16.3.
