# Do magnetic field lines indicate how a mangetic field will act on an “idealized” test magnetic north monopole?

We imagine an electric field and a magnetic field as vector fields.
When we are introduced to a static electric field, we usually picture it as an infinite number of vectors (magnitude,direction) in every point in space that will affect the movement ( or will exert a force) of any charged particle going thorough it.
So we can imagine how a test charge will follow (let's assume that the charged paricle field is negligible with respect to the "main" field) our electric/vector field.
Under this assumption, we usually draw field lines to represent how the field will act on a positive charge.
My question is the following:
When we draw magnetic field lines, are we describing how the magnetic field will act on an "idealized" test magnetic north monopole?

## 2 Answers

The magnetic field lines shows the directions along which little iron shavings line up. Each shaving become a magnetic dipole in the outer magnetic field, so the magnetic field lines describe how field will act on a test magnetic DIPOLE!

• Actually to me the magnetic field lines are identical to the ones of an "electric dipole" that indicates how that field act on a test positive charge – Gabriele Scarlatti Jul 8 '19 at 11:07
• However , there is a difference. Electric field will act on a test positive charge, even if it is motionless. But magnetic would not act on a motionless charge, action will be only if this charge moves. – Leiba Goldstein Jul 8 '19 at 11:15
• @GabrieleScarlatti Just an addition: If there were magnetic monopoles, the magnetic field would indeed act on a positive magnetic charge along these lines. But the thought process is similar on dipoles too, especially the part about shavings. Both are correct. – acarturk Jul 8 '19 at 11:40

Yes, you are correct. This is an example of electromagnetic duality --- if you swap electric fields and magnetic ones, and electric charges for magnetic monopoles, the laws of physics are the same*

*If there are time derivatives involved, there are some multiplicative factors of $$-1$$ due to the Lorentzian signature of spacetime. For the motion of test charges in static electromagnetic fields these do not arise.