Magnetic monopoles are hypothetical particles that possess only a single magnetic pole, either a north pole or a south pole, rather than the duality of north and south poles observed in regular magnets. In other words, they are isolated magnetic charges analogous to the electric charges found in particles like electrons and protons.
The concept of magnetic monopoles has been proposed to complete the symmetry between electricity and magnetism. In Maxwell's equations, which describe the fundamental principles of electromagnetism, electric charges and currents are sources of electric and magnetic fields. However, while electric charges come in isolated positive and negative forms, magnetic poles have only been observed in the form of dipoles (both north and south poles together) – never isolated north or south poles.
If magnetic monopoles existed, it would imply that magnetic fields could exist independently without always requiring both poles. This would provide a more symmetric description of electromagnetism, known as the "unified theory of electromagnetism." Grand Unified Theories (GUTs) and certain theories in string theory propose the existence of magnetic monopoles, although experimental evidence for their existence remains elusive.
As for their relation to electric charge, Dirac's quantization condition relates electric charge and magnetic charge (in case magnetic monopoles exist). This condition states that the product of electric charge (e) and magnetic charge (g) must be quantized in terms of the Dirac's quantum unit:
eg = n * (h / 2π)
Where:
e is the elementary electric charge,
g is the magnetic charge,
n is an integer, and
h is the Planck constant.
This relationship implies that if a magnetic monopole exists with a certain magnetic charge, it must be associated with a specific value of electric charge. This quantization condition provides a fascinating link between electric and magnetic charges, even though magnetic monopoles have not been definitively observed as of my last knowledge update in September 2021.