Question

Which Maxwell equation represents the non-existence of magnetic monopoles?

• A. \(\nabla \cdot \vec{E} = \frac{\rho}{\varepsilon_0}\)
• B. \(\nabla \cdot \vec{B} = 0\)
• C. \(\nabla \times \vec{E} = -\frac{\partial \vec{B}}{\partial t}\)
• D. \(\nabla \times \vec{B} = \mu_0 \vec{J} + \mu_0\varepsilon_0 \frac{\partial \vec{E}}{\partial t}\)

Hint:

\(\nabla \cdot \vec{B} = 0\) means magnetic field lines form {closed loops}, implying {no magnetic monopoles}.

Answer 1

The Correct Option is B

Concept: Maxwell’s equations describe the fundamental laws of electromagnetism. One of these equations states that the divergence of the magnetic field is zero. \[ \nabla \cdot \vec{B} = 0 \]
Step 1: Interpret the equation.} The divergence of a field measures the net flow of the field out of a point. If \[ \nabla \cdot \vec{B} = 0 \] it means magnetic field lines neither originate nor terminate at any point.
Step 2: Physical implication.} This indicates that magnetic monopoles do not exist. Magnetic field lines always form closed loops.
Step 3: Compare with other Maxwell equations.}

• Gauss’s law for electricity relates electric field divergence to charge density.
• Faraday’s law describes electromagnetic induction.
• Ampère–Maxwell law relates magnetic fields to current and changing electric fields.

Thus, the equation representing the absence of magnetic monopoles is \[ \nabla \cdot \vec{B} = 0 \]