How does a magnetic field collapse?

I have a basic question about magnetic fields, but the answer will help me better understand quantum collapse issues.

If the current in a wire is instantaneously shut off, what happens to the magnetic field that was present when the current was flowing? To be more specific:

Wire Point A Point B Point C Point D

When the current stops instantaneously, does the magnetic field disappear:

a. Simultaneously and instantaneously at points A B C and D.

b. At point A, then at point B, then at point C, then at point D (disappear outwardly from the wire at the speed of light).

c. At point D, then at point C, then at point B, then at point A (collapse back to the wire at the speed of light).

I realize that instantaneously shutting off the current in a wire is an unrealistic assumption, but for the sake of argument let’s go with it for now…

Thank you,

Bob

berkeman
Mentor
I realize that instantaneously shutting off the current in a wire is an unrealistic assumption, but for the sake of argument let’s go with it for now…
It's certainly non-physical, so it makes it harder to explain what is happening by using Maxwell's Equations and other math. In practical systems (like in flyback HV generating systems in CRT TVs), the current sink transistor is shut off very quickly, which causes the voltage across the B-field generating coil to "fly back" to a large voltage. The peak of this voltage is determined by the resonant capacitance in the system (an explicit capacitance in TV circuits, and parasitic capacitance in other situations where there is no explicit capacitor in parallel with the coil).

So a better way to set up the system you want to ask about is to say that the peak flyback voltage from opening the current drive to the coil is limited by some stray capacitance Cs. That will allow us to set up the math so you can see how the B-field generated by the wire or coil drops rapidly to low values (and or rings out as a damped sine wave, depending on the losses in the circuit).

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• Klystron and Dale
anorlunda
Staff Emeritus
When the current stops instantaneously, does the magnetic field disappear:

All real life circuits have some inductance. Therefore the current can never stop instantaneously, just as the voltage
##L\frac{dI}{di}## can never be infinite.

When you open a switch while it was carrying current, you'll see a spark. The spark dissipates energy from the magnetic field. Small sparks for small switches, big spark for big switches.

Circuit breakers are switches that are designed to not be damaged by the spark. In the video below, a switch that was not a circuit breaker was opened by accident while carrying current.

• Klystron, berkeman and Cryo
It's certainly non-physical, so it makes it harder to explain what is happening by using Maxwell's Equations and other math. In practical systems (like in flyback HV generating systems in CRT TVs), the current sink transistor is shut off very quickly, which causes the voltage across the B-field generating coil to "fly back" to a large voltage. The peak of this voltage is determined by the resonant capacitance in the system (an explicit capacitance in TV circuits, and parasitic capacitance in other situations where there is no explicit capacitor in parallel with the coil.

So a better way to set up the system you want to ask about is to say that the peak flyback voltage from opening the current drive to the coil is limited by some stray capacitance Cs. That will allow us to set up the math so you can see how the B-field generated by the wire or coil drops rapidly to low values (and or rings out as a damped sine wave, depending on the losses in the circuit).

Thank you for the reply. Without the involved math, I am handicapped. Nevertheless, given that the current goes from some value to zero via a complex path, my original question can be modified a bit to fit. Does the magnetic field (in concert with the changing current) go to zero simultaneously close to and far away from the wire, or does it go to zero close to the wire first, or does it go to zero furthest from the wire first?

DaveC426913
Gold Member
I have a diagram for that too. Attachments

• Nik_2213 and berkeman
• berkeman
tech99
Gold Member
I have a diagram for that too.

View attachment 237460
I had the impression that for a pure induction field, it can collapse instantly without a propagation delay. So the same must be true when it is built. For example, the magnetic field of a solenoid fills the Universe, yet it can discharge in a microsecond.
For two circuits coupled together by an induction field, as in a transformer for instance, we do not so far as I know experience a propagation delay. The two circuits operate as one.

• Robert Friz
DaveC426913
Gold Member
I had the impression that for a pure induction field, it can collapse instantly without a propagation delay. So the same must be true when it is built. For example, the magnetic field of a solenoid fills the Universe, yet it can discharge in a microsecond.
For two circuits coupled together by an induction field, as in a transformer for instance, we do not so far as I know experience a propagation delay. The two circuits operate as one.
If that were true, it would be an instant communication device.

The speed of light is effectively instant over short ranges. But mind that word 'effectively'.

Electromagnetism propagates at the speed of light.

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phyzguy
I had the impression that for a pure induction field, it can collapse instantly without a propagation delay. So the same must be true when it is built. For example, the magnetic field of a solenoid fills the Universe, yet it can discharge in a microsecond.
For two circuits coupled together by an induction field, as in a transformer for instance, we do not so far as I know experience a propagation delay. The two circuits operate as one.

These statements are not correct. Maxwell's equations are very clear on what happens. All changes to the fields propagate at the speed of light, as DaveC's diagram shows.

• berkeman
@DaveC426913 seems like you quote me at the wrong thread.

anorlunda
Staff Emeritus
I had the impression that for a pure induction field, it can collapse instantly without a propagation delay. So the same must be true when it is built. For example, the magnetic field of a solenoid fills the Universe, yet it can discharge in a microsecond.
For two circuits coupled together by an induction field, as in a transformer for instance, we do not so far as I know experience a propagation delay. The two circuits operate as one.

You may be confusing circuit analysis with fields as described by Maxwell's equation. One of the assumptions of circuit analysis specifically excludes magnetic fields extending outside the wires. That is the point of my Insight article, that many of us use circuit analysis while never understanding the assumptions that make it possible.

https://www.physicsforums.com/insights/circuit-analysis-assumptions/

DaveC426913
Gold Member
@DaveC426913 seems like you quote me at the wrong thread.
nyuk nyuk. Darned multi-quote. Fixed.

• Klystron, YoungPhysicist and berkeman
tech99
Gold Member
If that were true, it would be an instant communication device.

The speed of light is effectively instant over short ranges. But mind that word 'effectively'.

Electromagnetism propagates at the speed of light.
Of course, I agree, but I am trying to find an explanation for an apparent paradox where we have a pure induction field.

DaveC426913
Gold Member
Of course, I agree, but I am trying to find an explanation for an apparent paradox where we have a pure induction field.
Can you describe the scenario that presents the apparent paradox?
The scenario in post 7 is problematic, as pointed out.

tech99
Gold Member
Can you describe the scenario that presents the apparent paradox?
The scenario in post 7 is problematic, as pointed out.
If we have a solenoid carrying a current, its magnetic field extends outwards without limit. The magnetic field stores the inductive energy.
Now if I open the switch, the magnetic field collapses and develops a forward emf across the break. It delivers the stored energy back to the spark in maybe a nanosecond.
So the question is, how did the energy return from far away from the solenoid in a nanosecond?

anorlunda
Staff Emeritus
If we have a solenoid carrying a current, its magnetic field extends outwards without limit. The magnetic field stores the inductive energy.

Only if it has been carrying the same current for infinite time. Fields propagate in a vacuum at the speed of light.

If you have a 10 cm wide transformer, the propagation delay is about 20 picoseconds. It is real, but I doubt if you would notice it.

• Klystron
phyzguy
If we have a solenoid carrying a current, its magnetic field extends outwards without limit. The magnetic field stores the inductive energy.
Now if I open the switch, the magnetic field collapses and develops a forward emf across the break. It delivers the stored energy back to the spark in maybe a nanosecond.
So the question is, how did the energy return from far away from the solenoid in a nanosecond?

It's true that the magnetic field can extend to great distances. It does not extend to infinity unless the current has been running for an infinite time, as anorlunda pointed out. However, the energy density stored in the field is proportional to the square of the magnetic field, and the magnetic field outside the solenoid drops off as the cube of the distance away. So most of the energy stored in the field is stored very close to the solenoid. In fact for a long solenoid, most of the energy is stored inside the solenoid windings. So, since the speed of light is very fast, most of the energy returns to the solenoid windings very quickly.

• Nik_2213
Staff Emeritus