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 into 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...