# Electromagnetic inertia induced by surrounding charges?

1. Jun 1, 2012

### johne1618

Imagine that an electron is travelling 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?

2. Jun 1, 2012

### Jano L.

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

$$\mathbf E = - \frac{\partial \mathbf A}{\partial t} - \nabla \varphi.$$

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. Jun 5, 2012

### johne1618

This kind of argument has been made in the case of gravitation by Dennis Sciama to explain the mechanism of Mach's principle:

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. Jun 5, 2012

### Jano L.

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. Aug 9, 2012