Which Maxwell equation expresses Gauss's law for magnetism?

Which Maxwell equation expresses Gauss's law for magnetism?

• A. ∇×E = −∂B/∂t
• B. ∇·E = ρ/ε0
• C. ∇·B = 0
• D. ∇×B = μ0 J + μ0 ε0 ∂E/∂t

Answer: (C)

Magnetic fields have no isolated sources; their field lines form closed loops. Gauss's law for magnetism states that the net magnetic flux through any closed surface is zero, which is written as ∇·B = 0. This means there are no magnetic monopoles acting like sources or sinks for B, so the divergence of the magnetic field must vanish everywhere. This is different from Gauss's law for electricity, where the divergence of the electric field relates to the presence of electric charges. The other Maxwell equations describe how changing magnetic fields induce electric fields (Faraday’s law, ∇×E = −∂B/∂t) and how currents and changing electric fields produce magnetic fields (Ampere–Maxwell law, ∇×B = μ0J + μ0ε0 ∂E/∂t).

Magnetic fields have no isolated sources; their field lines form closed loops. Gauss's law for magnetism states that the net magnetic flux through any closed surface is zero, which is written as ∇·B = 0. This means there are no magnetic monopoles acting like sources or sinks for B, so the divergence of the magnetic field must vanish everywhere.

This is different from Gauss's law for electricity, where the divergence of the electric field relates to the presence of electric charges. The other Maxwell equations describe how changing magnetic fields induce electric fields (Faraday’s law, ∇×E = −∂B/∂t) and how currents and changing electric fields produce magnetic fields (Ampere–Maxwell law, ∇×B = μ0J + μ0ε0 ∂E/∂t).