# Propagation Of Magnetic Fields

It my understanding that it takes two fields to propagate through space, electric and magnetic, but what about a magnetic field created when a solenoid is energized with direct current?

How exactly does that magnetic field travel? There is no frequency involved with direct current. What determines the extent of the magnetic field before it collapses?

Finally, what about permanent magnets. How do they propagate? There is no frequency here either.

To summarize my questions: How do magnetic fields get from point A to point B without a frequency and collapsing fields?

Thanks

It my understanding that it takes two fields to propagate through space, electric and magnetic,

This is the electromagnetic wave that travels with velocity c.

but what about a magnetic field created when a solenoid is energized with direct current?

At the moment of starting the direct current the field around the solenoid expands , with velocity c and then becomes static, not detectable unless a test magnet moves .

How exactly does that magnetic field travel? There is no frequency involved with direct current. What determines the extent of the magnetic field before it collapses?

The magnetic field does not travel . It just is. Fields are like a coordinate system that is needed to describe the mathematics of moving magnetic and electric charges.

Finally, what about permanent magnets. How do they propagate? There is no frequency here either.

Frequency is an attribute of electromagnetic waves. The field of the magnet can only be detected if something charged or magnetized moves (second page), and the effects can be measured

To summarize my questions: How do magnetic fields get from point A to point B without a frequency and collapsing fields?

Because it is a mathematical construct that allows to be able to calculate the behavior of moving magnetic and electric charges, successfully, to a great accuracy.

This explanation is in the classical electromagnetic theory.

The story is more elaborate going to quantum electrodynamics, but beyond the scope of this question.

Associating the curl of a magnetic field with rate of change of electric field, and the curl of an electric field with the rate of change of a magnetic field, is extremely useful, but not necessary.

[Note: the time derivative of the electric field does not cause a magnetic field, it causes the curl of a magnetic field, which is a big difference.]

In the Jefimenko formulation of electromagnetism, the electric and magnetic fields at $$(\vec r, t)$$ are entirely caused by charges, currents, and their time derivatives...all at positions $$\vec r'$$ consistent with the retarded time:

$$t_r = t - \frac{|\vec r-\vec r'|}c$$

There is no need to consider the state of the electric field when computing the magnetic field (and vice versa).

With that view point, a magnetic field some distance from a dipole, looks like a dipole field provided:

$$\frac{|\vec r-\vec r'|} c < t-t_r$$

Moreover, if you do consider the standard formulation with Maxwell's equations, it's important to consider what part of the field is radiative, and what is near-field. The dipole (magnetic) field of a bar magnet, $$\vec m$$:

$$\vec B(\vec r) =\frac{\mu_0}{4\pi} \big[ \frac{3\hat r(\hat r\cdot\vec m) -\vec m}{r^3} \big]$$

falls as $$1/r^3$$. The energy falls as $$1/r^6$$, and is not radiative.

• Ooh, +1 for an explanation based on Jefimenko’s equations! Nice – Dale Jan 21 at 4:20

what about a magnetic field created when a solenoid is energized with direct current? ... There is no frequency involved with direct current.

There is no frequency involved with steady direct current, but you are describing a switched direct current. This is also known as a step function, which does have frequency content at all frequencies: https://mathworld.wolfram.com/FourierTransformHeavisideStepFunction.html

what about permanent magnets. How do they propagate?

As you move a permanent magnet the changing B field produces an E field by Faraday's law. From there you have standard propagation of an EM wave.

• But when the magnet is stationary it still has a field that propagates away from the magnet, right? How does that field travel? Thanks – Lambda Jan 21 at 3:43
• If the magnet is stationary then there is no field propagation. Static fields do not propagate, by definition – Dale Jan 21 at 3:54