# Question about Rutherford atomic model

1. Sep 1, 2010

### Taturana

Rutherford postulated that the electrons are moving around the nucleus of the atom in circular trajectories, right?

My professor said that or I believe in it or there is no more chemistry to study, because this does not agree with some law of Maxwell's theory of electromagnetism.

He said that this (the fact that the electrons moves in circular trajectories around the nucleus) violates a law of Maxwell that states that "every moving charge that is in a electric field loses energy".

The electric field is the one generated by the positive charges in the nucleus (protons). And the electrons are moving inside this electric field so they must lose energy, but it does not happens according to Rutherford atomic model.

My question is: the electrons are moving circularly around the nucleos, so their trajectory is in a equipotential path (has equal potential in all points) because every circular trajectory forms 90 degrees with all field lines that comes out from the nucleus; so why must the electron loose energy?

Thank you,
Rafael Andreatta

2. Sep 1, 2010

3. Sep 1, 2010

4. Sep 1, 2010

### granpa

because the field is changing

5. Sep 1, 2010

### Taturana

is the electric field generated by the nucleus changing? why?

6. Sep 1, 2010

### Studiot

I think he probably said every accelerating charge loses energy.

Anything moving at constant speed in a circular path is constantly accelerating.

7. Sep 1, 2010

### Taturana

Hum, this makes sense... but could you explain-me more clearly? I accept that anything moving at constant speed in a circular path is accelerating (because of centripetal acceleration, right?), but I don't understand why the electron would loose energy if it is moving along a equipotential path... (The circular trajectory is an equipotential path, right?)

Thanks

8. Sep 2, 2010

### Anamitra

When a charge moves[for example the moving electron in this problem] the electric field at any fixed point changes.Due to change of the electric field a magnetic field is created and the resulting Poynting vector radiates energy.Now this radiation comes from the Kinetic energy of the charge itself and so it has to retard.
Abraham Lorentz Formula[for radiation reaction] : F(radiation)=1/[4pi epsilon(0)] (2/3)(q^2/c^3)[Rate of change of acceleration]

There is another interesting issue related to the "self retardation of a charge".Consider a spherical charge distribution. The charges at different parts of this distribution exert forces ,on each other ,that cancel out.But when a charge accelerates, these forces do not cancel.This can be shown by calculation considering the "finite speed of signal propagation" as we know from Special Relativity.For one part to be aware of the motion of the other it takes some time. [It can be shown that for uniform motion the cancellation continues]You will find this in Feynman's Lectures,Second Volume,Chapter 28,Electromagnetic Mass,Section 28-4,The Force of an Electron on Itself.

Last edited: Sep 2, 2010
9. Sep 2, 2010

### Studiot

Charges moving with unvarying velocity do not loose energy by radiation. Beta radiation will continue forever unabated if left undisturbed.
Charges subject to varying velocity ie accelerating do radiate EM energy.

There are plenty of refernces on the net including video giving all the gory details, which should also be in you electrodynamics book.