Time derivative jump of the electric/magnetic field

In summary, Maxwell's equations imply that electric and magnetic fields can have time derivatives, and this might be a problem if electric and magnetic charges are not conserved.
  • #1
vogtster
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So I just wanted to see if anyone could offer some suggestions. So in my mind this seems impossible, in the case of electric field a jump in time derivative of that field would indicated in my mind that electric charge was either introduced or removed from the system instantaneously which would violate conversation of electric charge. If you prescribe to the quantum mechanic perspective that magnetic charge exists, the same argument would hold the magnetic field, since magnetic charge would also have to be conserved. If you just assume gausses law of magnetism holds, then again, this would mean a magnetic monopole would be introduced to the system, which is also problematic.
I'm not sure if there is a rigorous mathematical argument for this though - or if this is just true based on empirical observation (similarly how gausses law of magnetism is derived)
I would very much appreciate some comments on this subject.
 
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  • #2
What about a radio wave encountering a wall?
 
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Likes sophiecentaur
  • #3
Maxwell's Equations include equations for the time derivatives of both the electric and magnetic fields. What do they imply about your question?
 
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Likes berkeman
  • #4
Coincidentally I have a similar doubt but probably it comes from a different perspective. The boundary conditions proposed for electromagnetic fields consider only a spatial normal term. But I want to know what happens with the jump in an arbitrary spacetime surface. Mathematically, we know what happens when we dot and cross a purely spatial vector with the jump of the electromagnetic field, but what happens when we dot and cross with a time vector? For instance, we ask: for the electric field at a given instant to another instant, what is the jump between a media that changes its properties at that point (maybe a nonlinear material)? In the formalism of Clifford Algebra (See John W. Arthur - Understanding Geometric Algebra for Electromagnetic Theory), I ask

$$ \vec{e}_t (E_2 - E_1) + \vec{e}_t (B_2 - B_1) = ? $$

Where ## E_2 ## and ## B_2 ## are the electromagnetic fields at the same spatial point of ## E_1 ## and ## B_1 ## but at an infinitesimal instant after. This is analogous to the jump between two material medium in space, but with the normal being a time vector.

Maybe we can derive something like this by applying the integral laws and considering a jump in ## \varepsilon ## and ## \mu ## from a given instant to another. Of course, this implies changing the constitutive laws of the material. In a similar spirit of the space normal, probably it will be a function of a charge and a current surface density (which in our spatial notion should appear as a sudden volumetric change of current or charge).

I physically think it's obvious that in a medium free of charges, the fields should be continuous, changing only speed of propagation. But maybe we need a more rigorous treatment just to be sure. Considering that charges cannot disappear, the situation where ## \rho ## would peak at a given volume would be physically impossible, but maybe a change in current?

Maybe this can give a new perspective to your problem.
 

1. What is a time derivative jump of the electric/magnetic field?

The time derivative jump of the electric/magnetic field refers to the sudden change in the rate of change of the electric or magnetic field over time. This jump can occur at boundaries between different materials or in response to changes in the environment.

2. How is the time derivative jump of the electric/magnetic field measured?

The time derivative jump of the electric/magnetic field is measured using instruments such as oscilloscopes, which can detect changes in the electric and magnetic fields over time. These changes can be graphed and analyzed to determine the magnitude and direction of the time derivative jump.

3. What causes a time derivative jump of the electric/magnetic field?

A time derivative jump of the electric/magnetic field can be caused by a variety of factors, including changes in the material properties, the presence of electric or magnetic fields from external sources, and the movement of charged particles. It can also occur due to sudden changes in the environment, such as lightning strikes or power surges.

4. How does the time derivative jump of the electric/magnetic field affect electronic devices?

The time derivative jump of the electric/magnetic field can have a significant impact on electronic devices, as it can cause sudden changes in the electric and magnetic fields that can disrupt the normal functioning of the device. This can lead to malfunctions, damage, or even failure of the device if it is not properly protected.

5. Can the time derivative jump of the electric/magnetic field be controlled or mitigated?

While the time derivative jump of the electric/magnetic field cannot be completely eliminated, it can be controlled and mitigated through the use of protective measures such as shielding and grounding. These measures can help to reduce the impact of sudden changes in the electric and magnetic fields on electronic devices and prevent damage or malfunctions.

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