# What exactly is magnetic flux?

It is intuitive to think of an electric field, which describes the variance in the force acting on a charged particle if it were located in a certain position. However it is not so easy to understand what magnetism is and what flux is. Apparently magnetism is an effect of special relativity for moving charges, but this is also hard to understand. What is magnetic flux?

• Are you saying you understand what electric field flux is but not magnetic field flux? – BioPhysicist Nov 5 '18 at 17:28
• electrostatic interaction a "line" phenomenon, magnetostatic interaction is a "surface" phenomenon. – hyportnex Nov 5 '18 at 17:32
• Welcome "New contributor* Mark! I wonder if you're not quite clear on the distinction between field and flux (of that field through a surface). We have the electric field and magnetic field and then we have electric flux and magnetic flux. So, are you asking about the magnetic field or magnetic flux? – Alfred Centauri Nov 5 '18 at 17:43

It is intuitive to think of an electric field, which describes the variance in the force acting on a charged particle if it were located in a certain position

The electric field $$\mathbf E$$ is actually just a force per unit charge $$(q\mathbf E=\mathbf F)$$, where $$q$$ is the charge the electric force is acting on. It does not describe a variance of a force.

However it is not so easy to understand what magnetism is and what flux is. Apparently magnetism is an effect of special relativity for moving charges, but this is also hard to understand. What is magnetic flux?

So it is true that electric and magnetic fields can be viewed as parts of the same thing in SR, but this view is not needed to understand magnetic flux. Similar to our above discussion about $$\mathbf E$$, the magnetic field $$\mathbf B$$ can also be described by the force it exerts on a charged particle moving with velocity $$\mathbf v$$. $$\mathbf F=q\mathbf{v}\times\mathbf{B}$$

A good way most introductory physics classes explain the direction of the magnetic field is that it points in the direction a compass would point. Of course, we can determine the entire (magnitude and direction) magnetic field from its current sources using the Biot-Savart law in the same way we can determine the electric field from its charge sources using Coulomb's law, but this is not the crux of your question.

Magnetic flux is a specific case of the more general idea of the flux of a vector field $$\mathbf V$$, whose origin comes from fluid dynamics. The flux $$\Phi$$ of a vector field across some surface is given by the surface integral $$\Phi=\int \mathbf V\cdot\text{d}\mathbf A$$

Where $$\text{d}\mathbf A$$ is an infinitesimal area element vector whose direction is normal to the surface.

This can be applied to the magnetic field, where then you would just replace $$\mathbf V$$ with $$\mathbf B$$. Flux tells you "how much field is flowing through the surface". Since the integral depends on the dot product $$\mathbf V\cdot\text{d}\mathbf A$$, you can see that if the field is normal to the surface then we get maximum flux (maximum flow), but if the field is parallel to the surface we get no flux (no flow).

• So the electric field is force per charge. Can this be represented in a visual way. Hmmm, well the force varies with a radius from a charge right? As you increase the radius, the force exerted on a charge decreases. Also, how can the field flow, since the field is not an actual thing, rather an abstract explanation, for the force experienced by a charge. – Mark Nov 5 '18 at 18:37
• @Mark That's why I use quotation marks and parentheses. The idea of flux was originally used for fluids, where the vector field described an actual physical flow of fluid. Of course there isn't an actual flow for magnetic flux, but you can think of it in the same way. – BioPhysicist Nov 5 '18 at 19:03
• @Mark Also note that the electric field is a force per unit test charge (charge the force acts on) not force per unit source charge (charge that creates the electric field). – BioPhysicist Nov 5 '18 at 22:37