It should work fine with theta/phi, i'm not sure the motivation to convert to Cartesian it seems to me that would be an ambiguous conversion.
A_{lm} = \int Y^*_{lm}(\theta, \phi) g(\theta, \phi) d\Omega
g(\theta, \phi) = \sum_{l=0}^{\infty}\sum_{m=-l}^{l} A_{lm} Y_{lm}(\theta, \phi)
For...
It's true, impulse is a change in momentum, and momentum and energy can have a correlation. However, you'd need to be careful because the force in a chain may not be the same as the total force on the bicycle. First, just because there is tension in a chain doesn't mean its actually doing...
Thank you for your reply. However, \nabla A = \nabla \cdot A + \nabla \wedge A = \nabla \wedge A, from the lorenz condition \nabla \cdot A = 0.
I think I realized where the negative comes in. EG:
(\partial_0 A^1 + \partial_1 A^0)\gamma_0 \gamma_1 = (\partial^0 A^1 - \partial^1...
Hi. I've been learning how to use geometric algebra and I've been stumbling when I apply it to E&M. I am hoping someone here can point out what I am doing wrong.
The problem comes when trying to represent the field tensor in terms of the 4-potential. Here is the standard form:
F^{\mu\nu}...
You have the two conservations, in vector form:
Energy:
\nabla \cdot S + J \cdot E + \frac{\partial u}{\partial t}= 0
Momentum:
[\frac{\partial S}{\partial t} + \rho E + J\times B]_i - \frac{\partial T_{ij}}{\partial x_j} = 0
S = poynting vector (viewed as energy flux...
you can integrate vxB (where v is the velocity of the wire) along the wire to find the motional emf which will oposes the emf put into the wire to drive it forward.
You would view this as an inelastic collision. Yes, momentum is conserved. The collision will occur over some amount of time giving you what's called an impulse. force = momentum/time. So, the force between the box and cart acts over some delta time. Equal and opposite means force on box and...
You need to be a student of this instead of an authority. You are the one who is wrong. I am trying to make this simple because you have no background in physics. But I can see there is no point in trying to explain it further. Please try to study electromagnetism for yourself in the texts...
It does consume electrical fields, because that is what you put in to move the electrons. That's why you need to supply power to maintain the electric field. Otherwise it would be used up, disappear, and work would cease to occur.
DRUM, if magnets did work then motors would not require any electrical energy to run, except for a small resistance in the wire, and conversely a permanent magnetic would lose all magnetism almost instantly because its magnetic energy would be consumed in doing work on the rotor. People have...
It's a power law problem. Our brains had to evolve with a certain scale of objects where the wave nature is irrelevant to us in survival, at least until the last hundred years where we could see it. If we could have evolved in the quantum world it might seem weird that objects could retain...
It *could* increase physical resistance if the wire gets stretched at all during the winding process. Stretching both decreases cross-sectional area AND increases length, both of which would act to increase resistance.
A charge with uniform velocity will have a different electric, and magnetic field than a stationary charge. The magnetic field is easy to understand if you view the moving charge as a current. The electric field change can be understood by lorentz contraction of the electric field lines. The...
I just wanted to state one last thing here. You cannot *always* completely transform away magnetic field. This is one situation where that is true, because you cannot take a pure magnetic field, and turn it into a pure electric field, by lorentz transformation. However, you can always transform...
The shape of the magnetic field lines has nothing to do with this. I will try to explain this without vector algebra. Your picture is only valid for a static situation which by definition has no work associated with it. To understand what happens when the wire actually moves, you need to look at...
Those are the equation of motion for charged particles and power delivered to them. Why would they go back to original positions? Work has to do with change of ENERGY, not position. The magnetic force is not a conservative force, for no other reason that it does no work in the first place. The...
How does that violate quantum physics? You are saying at some large distance from a source you would no longer be able to make a measurement of the electric field?
A square looks rectangular in another frame but its the same object. Just because they look different doesn't mean they are different. It's called lorentz covariance. You can describe an object and what it looks like in every frame.
And no I did not even write field potentials (phi and A I...
Well, energy/momentum is something, or represents the effect of something. And whatever that something is everything is made of it.
My interpretation/speculation (and that is all it is) is that "something" is structures in space-time. Or, in another way, alterations to space-time. We see that...
I mean in terms of work. obviously jxB does no work because j*(jxB) = 0. So magnetic force does no work, in only changes momentum. Mechanical power transfer comes from J*E at a fundamental level so saying the power comes from magnetic force is misleading it comes from the electrical force...
we want to find the maximum of E^{2}
speculate it is where the laplacian is non-zero.
something like:
\nabla^{2}(E\cdot E) = \nabla\cdot(\nabla(E\cdot E)) = \nabla\cdot(2( (E\cdot\nabla)E + E\times(\nabla \times E))) = 2(E\cdot\nabla)\nabla\cdot E = 2(E\cdot\nabla)\rho
\nabla \times E = 0...
If I had to pick one it would be statement E. Once the wires are moving toward each other then jxB (or vxB) no longer points toward the other wire (to the right).
There is a missing statement that the current I is held constant. If you have two free interacting currents, say both I_{z}, they will move toward each other. But now the z component is different for each: I_{z}^{'} < I_{z}. Kinetic energy is not changed. What changes is the distribution of EM...
Just take the limit where a long pipe intersects perpendicular to the parallel plates. The field will be zero inside the pipe (because the potential is everywhere uniform there), except at the edge where you have fringing fields. Now every field line has to go between potentials (E=-dV/dx), so...
What is measurement except just a series of locations of events in time and space. The ideas of charge, fields, or photons are just models to predict (or explain) distance/correlation between events: modification of distance if you will. One might consider GR more elegant because it uses...