Magnetic monopole

Problem

Suppose an isolated “north” type magnetic charge existed. Which Maxwell equation would be modified? What would happen near a compass? Sketch qualitatively the $\vec B$ field lines around the monopole.

Solution

Gauss’s law for magnetism would be modified. Currently it states $\nabla\cdot\vec B = 0$ (absence of magnetic charges, zero flux through any closed surface); with a monopole of density $\rho_m$ it would become: $\nabla\cdot\vec B = \rho_m$ and the flux of $\vec B$ through a closed surface enclosing the monopole would no longer be zero.

The $\vec B$ field lines would radiate outward from the north monopole, exactly as $\vec E$ field lines emerge from a positive electric charge. A compass placed nearby would point radially, towards or away from the monopole, instead of following the usual dipolar pattern. $\ev{\nabla\cdot\vec B = \rho_m;\ \text{radial lines emerging from the monopole}}$

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Topics: Magnetismo Concepts: Campo magnetico Skills: Analisi di casi limite e fantafisica