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in all my physics courses I have been told that magnetic field lines are absolutely closed lines. It is well explained in this wikipedia page, which states:

A magnetic field has no sources or sinks (Gauss's law for magnetism), so its field lines have no start or end: they can only form closed loops, extend to infinity in both directions, or continue indefinitely without ever crossing itself.

It is equivalent to the statement:

$$\nabla \cdot \mathbf B=0$$

But there are many situations in which equivalent magnetic charges are introduced:

$$\nabla \cdot \mathbf B=\rho_{\text{m}}$$

Magnetic charges and magnetic currents are often used to model a certain system in an equivalent way which leads to simplest calculations. For instance, a magnetic dipole antenna is seen as made of two magnetic charges, one positive and one negative, that alternates in time (it is the dual structure of Herzian dipole). So, in simple words: magnetic charges do not exist, but there are many real systems that act like them and so it may be useful to model them with magnetic monopoles, because this analysis is easier.

Now my question is: consider one of this system which behaves as a magnetic charge. What will its magnetic field lines be? I'd say that they won't be closed loops, since for the whole system we may write:

$$\nabla \cdot \mathbf B=\rho_{\text{m}}$$

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You're correct they won't be closed loops. Instead they'd look like diagrams of electric fields. Note the equations would be very similar then: you can get Gauss's law for the electric field by replacing $\vec{B}$ with $\vec{E}$, and $\rho_m$ with $\rho_e$, and shifting some constants. Intuition for electric fields carries over to magnetic fields, in that case.

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