Maxwell's equations and the momentum of charge

There appears to be a conservation of charge momentum (qv) analogous to that for mass (mv) although in the case of charge it is more potential in nature. A change in the flow of charge (or current) produces changing magnetic and electrics fields according to Maxwell's equations. These in turn tend to produce an equal and opposite flow of charge (or current).

There isn’t.

Sirius Q said:

There appears to be a conservation of charge momentum (qv) analogous to that for mass (mv) although in the case of charge it is more potential in nature. A change in the flow of charge (or current) produces changing magnetic and electrics fields according to Maxwell's equations. These in turn tend to produce an equal and opposite flow of charge (or current).

To see there isn't, consider two objects with equal and opposite charge, but different masses, initially at rest. Conservation of momentum is incompatible with conservation of "charge momentum".

In fact, to conserve the initial zero value of charge momentum, two opposite charged particles initially at rest would have to move in the same direction under their mutual influence. E.g. if ##q_1 = -q_2##, then we must have ##\vec v_1 = \vec v_2##. Which contradicts that the charges attract.

Is there a question here?

PeroK said:

To see there isn't, consider two objects with equal and opposite charge, but different masses, initially at rest. Conservation of momentum is incompatible with conservation of "charge momentum".

In fact, to conserve the initial zero value of charge momentum, two opposite charged particles initially at rest would have to move in the same direction under their mutual influence. E.g. if ##q_1 = -q_2##, then we must have ##\vec v_1 = \vec v_2##. Which contradicts that the charges attract.

Thank you for your analysis of the motion caused by the mutual attraction of two particles with equal and opposite charge but different masses, but what about the changing magnetic and electric fields produced by the motion of the charged particles which can in turn produce motion of charged particles?

Sirius Q said:

Thank you for your analysis of the motion caused by the mutual attraction of two particles with equal and opposite charge but different masses, but what about the changing magnetic and electric fields produced by the motion of the charged particles which can in turn produce motion of charged particles?

What about it?

Sirius Q said:

what about the changing magnetic and electric fields produced by the motion of the charged particles which can in turn produce motion of charged particles?T

Those fields aren’t charged, so their presence or absence doesn’t affect the value of ##qv##, the quantity you suggest is conserved but is not in the counterexamples provided by @PeroK.

Sirius Q said:

There appears to be a conservation of charge momentum (qv) analogous to that for mass (mv) although in the case of charge it is more potential in nature. A change in the flow of charge (or current) produces changing magnetic and electrics fields according to Maxwell's equations. These in turn tend to produce an equal and opposite flow of charge (or current).

I recommend that you get hold of a copy of "Classical electricity and magnetism" by Wolfgang Panofsky and Melba Phillips. Maxwell's equations only describe the divergence and curl of the electric and magnetic field vectors E and B in terms of static charge, current and each other. They make no mention of force, momentum or mass flow. To see these you need to look first at the Maxwell stress tensor and the Poynting vector. This leads to Einstein's relativistic electromagnetic stress energy momentum tensor, which has units of pressure, and where the Poynting vector E X H is divided by the speed of light to give the electromagnetic momentum density at a point in space at an instant in time. When the tensor is differentiated with respect to space, the units of the derivative of the momentum density terms have the units of mass flow. When the tensor is differentiated with respect to time, the units of the derivative of the momentum density terms have the units of force. These equations are easier to admire than to solve!

There certainly is some analogy here, but try to work it out from these formulas

F = q(E + v × B)

and the analogous one for mass. This is the natural starting point. Also relevant is the formula for the energy in the electromagnetic field E² - B².

E/m where E is the energy in the electromagnetic field, might be related to mv/m = v.

my guess is that the analog of mv is q(E² - B²), or something nearly the same.

Nugatory said:

Those fields aren’t charged, so their presence or absence doesn’t affect the value of ##qv##, the quantity you suggest is conserved but is not in the counterexamples provided by @PeroK.

Transmitters produce electromagnetic waves that carry no charge but have the potential to produce a motion of charge in a receiver.

Sirius Q said:

Transmitters produce electromagnetic waves that carry no charge but have the potential to produce a motion of charge in a receiver.

So what? This doesn’t change thd fact that there are direct counter examples to your idea of qv being a conserved quantity.

Thread closed temporarily for Moderation...

Sirius Q said:

There appears to be a conservation of charge momentum ...

Your mistaken speculations have been addressed. The thread will remain closed.