Which equation demonstrates that there are no magnetic monopoles?

Which equation demonstrates that there are no magnetic monopoles?

• A. ∇×E = 0
• B. ∇·B = 0
• C. ∇×B = 0
• D. ∇×E = -∂B/∂t

Answer: (B)

Magnetic fields have no starting or ending points; they form closed loops. This is captured by Gauss's law for magnetism: the divergence of B is zero everywhere. If magnetic monopoles existed, a point in space would act like a source or sink of magnetic field, giving a nonzero divergence at that point. So ∇·B = 0 expresses there are no magnetic charges. The other equations describe how electric and magnetic fields interact in different situations—Faraday’s law says a changing magnetic field creates an electric field, and Ampere–Maxwell’s law links the curl of B to currents and changing E. A zero curl of B, or an E field that is always conservative, would be far too restrictive and doesn’t specifically encode the absence of magnetic monopoles.

Magnetic fields have no starting or ending points; they form closed loops. This is captured by Gauss's law for magnetism: the divergence of B is zero everywhere. If magnetic monopoles existed, a point in space would act like a source or sink of magnetic field, giving a nonzero divergence at that point. So ∇·B = 0 expresses there are no magnetic charges.

The other equations describe how electric and magnetic fields interact in different situations—Faraday’s law says a changing magnetic field creates an electric field, and Ampere–Maxwell’s law links the curl of B to currents and changing E. A zero curl of B, or an E field that is always conservative, would be far too restrictive and doesn’t specifically encode the absence of magnetic monopoles.