Electromagnetic inertia induced by surrounding charges?

In summary, when an electron is moving uniformly in a charged sphere, it experiences an induced electric field that causes it to feel a force in the opposite direction of its motion.
  • #1
johne1618
371
0
Imagine that an electron is traveling with velocity +v inside a uniform sphere of charge at potential +V.

In the rest frame of the electron the charged sphere has velocity -v.

Thus in the rest frame of the electron, inside the charged sphere, there is a vector potential A given by

A = - V/c^2 v.

Now imagine that one applies a force to accelerate the electron to dv/dt.

In the electron's instantaneous rest frame there will be an induced electric field E given by

E = - dA / dt

E = V/c^2 dv/dt

The electron will feel an induced retarding force given by

F = -e E

F = -eV/c^2 dv/dt

Thus the charged sphere induces a kind of electromagnetic inertia on the electron.

Is this reasoning correct?
 
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  • #2
The uniform motion is possible only if the uniformly charged sphere is made from a dielectric, so that its charge does not move. For the metal sphere, the charge inside will feel net attracting force towards the wall.


If the particle moves uniformly (total force being zero), the electric field in its rest frame is given by

[tex]
\mathbf E = - \frac{\partial \mathbf A}{\partial t} - \nabla \varphi.
[/tex]

Both terms are zero, so there is no electric field inside the sphere.

Now, if there is another external force, this alone determines the acceleration of the particle. There is no force due to charge at the surface of the sphere - for accelerating particle, the above formula is not valid.
 
  • #3
This kind of argument has been made in the case of gravitation by Dennis Sciama to explain the mechanism of Mach's principle:

http://adsabs.harvard.edu/abs/1953MNRAS.113...34S

He assumed Maxwell-type equations valid for weak gravitational fields.

I was just wondering if the analogous electromagnetic inertia effect could be tested in the laboratory.
 
  • #4
That is a very interesting paper, thank you for the reference.


In the case with charge inside charge dielectric sphere, similar argumentation, although completely contradicting electromagnetism and relativity, leads to the force you wrote above. This force seems to modify inertial mass of the charge.

Of course, such effect could be in principle tested. For V = 1 million Volts (van de Graaf generator can achieve that), the mass change is

delta m = eV/c^2 ~10^-30 kg,

which is of the order of mass of the electron! So the effect appears to strong enough to be measurable on electrons:-) If it is there, I think it would be in complete contradiction to electromagnetic theory and relativity...
 
  • #5
What do others think about this argument?
 
Last edited:

1. What is electromagnetic inertia induced by surrounding charges?

Electromagnetic inertia induced by surrounding charges is the phenomenon where the motion of an object is affected by the presence of other charged objects in its surroundings. This is due to the electromagnetic forces exerted by the surrounding charges on the object.

2. How does electromagnetic inertia induced by surrounding charges affect the motion of an object?

Electromagnetic inertia induced by surrounding charges can either increase or decrease the inertia of an object, depending on the direction and strength of the electromagnetic forces. This can either speed up or slow down the object's motion.

3. Is electromagnetic inertia induced by surrounding charges a significant factor in everyday life?

Yes, electromagnetic inertia induced by surrounding charges plays a significant role in everyday life. It is responsible for the functioning of many electronic devices, such as motors and generators, and also affects the motion of charged particles in electromagnetic fields.

4. Can electromagnetic inertia induced by surrounding charges be manipulated or controlled?

Yes, it is possible to manipulate or control electromagnetic inertia induced by surrounding charges. This can be achieved through the use of external electromagnetic fields to counteract or enhance the effects of surrounding charges on the object's motion.

5. Are there any practical applications of electromagnetic inertia induced by surrounding charges?

Yes, there are many practical applications of electromagnetic inertia induced by surrounding charges. These include the development of more efficient motors and generators, as well as the use of electromagnetic levitation in transportation systems. It also plays a crucial role in the functioning of various electronic devices, such as speakers and computer hard drives.

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