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A magnetic monopole is a hypothetical particle with only one magnetic pole. Their magnetic fields would not be divergence-less. Predicted by certain modern theories, including string theory, supergravity, and various popular grand unified theories.

In Maxwell's equations, Gauss's law for magnetism states that:

$$\nabla\cdot\vec B=0$$

Whereas the corresponding law for electricity states that:

$$\nabla\cdot\vec E = \frac{q}{\epsilon_0}$$

This obvious asymmetry between the above two equations, that there is no "magnetic charge", as there is an "electric charge", indicates that it is pfossible that there in fact are, magnetic charges, and thus magnetic monopoles.

See also this meta post [1]

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