Actually, the potential going to zero at infinity is just a convention to make the math easier. If you placed your system in a giant metal box (giant enough to be considered out at infinity) and held the box at a potential V, the problem would go to V at infinity and not zero. When you work with...
Static fields, by definition, don't propagate. If you have an initially static field, and a change occurs, you no longer have a static field. You now have a regular electrodynamic field and the change propagates out at the speed of light in the material just like all propagating electrodynamic...
An oscillating dipole cannot radiate along its axis (you can convince yourself of this by drawing a charge bobbing up and down with the electric field lines attached at different points in time). For the one polarization, the axis of the induced dipoles lines up with the reflected ray at...
Dark matter is the gravitational glue that keeps galaxies from flying apart. Without dark matter, most galaxies would not have enough mass to create enough gravity to keep it in one piece. Dark matter gives enough extra mass to do the trick. Dark matter is not just dust or gas. You can see dust...
A short circuit sends more current than expected to parts of the circuit, causing them to physically burn out as they are not designed to handle such a load. If you opened up the phone, you may even see burn marks and melted plastic on the circuit board. Replacing the burned out circuit...
If earth were perfectly rigid, then yes, in principle, you spinning on a chair would cause the earth to spin in the opposite direction to conserve momentum. But the earth is so huge compared to you that the change in spin the earth would experience is so small it would just get overpowered by...
No, you need the fields for a complete description of electromagnetic. The fields exist in their own right. How can you describe an isolated electromagnetic wave in free space without using fields? The force construction replacing the fields construction only works when you are talking about the...
Yes of course. I have in fact experienced this. I had a pedal bike with a headlamp that was powered by a little generator attached to the wheels. Whenever I turned on the headlamp, the wheels a little harder to push. Of course it should because you can't create energy out of nothing. I...
More accurately: The electric field in a perfect conductor at equilibrium is zero. There are no perfect conductors in real life, so the field always pokes in a bit. But this is an excellent approximation for many conductors. Also, you have to have perfect equilibrium to give all the excess...
It's called the law of conservation of mass/energy. Matter/energy cannot be created or destroyed, but only transformed into different states. The total matter/energy in a closed system must stay constant. That is what the equation means. The c is just to make the units work. In naturalized...
"I was always told that the physics of these ride designs made it so that the people would be safe even without a restraint." You were told wrong. That used to be true of many of the older, safer, slower rides. As an extra precaution, designers aligned the g-forces to keep a person in their seat...
sweet_springs: Gauge freedom is not a result of some kind of redundancy in Maxwell's equations for the fields, because there is no redundancy in Maxwell's equations for the fields. Gauge freedom is a result of the fact that we are defining the fields in terms of something else non-physical (the...
I know this thread is old but I have done some analysis and I need to correct my earlier comments. Maxwell's equations contain six unknowns: Ex, Ey, Ez, Bx, By, Bz and seem to contain a linear set of differential equations consisting of 8 scalar equations. The problem therefore seems...
- Suck all the air and dust out of a given volume and you have a classic "vacuum", but you still have solar neutrinos shooting through (among other things).
- Shield the solar neutrinos (good luck), and you still have cosmic rays (among other things).
- Shield the cosmic rays, and you still have...
The point is that cosmic expansion itself does not stop. Space itself is everywhere expanding, even here on earth. But as the earth is bumped slightly father away from the sun due to cosmic expansion, it does not have the velocity to sustain a higher orbit, so it returns to its original distance...
Although I enjoy this back and forth debate, it's a bit like arguing how many angels can fit on the head of a pin. Any idea that is not falsifiable through tests or observations is just speculation. And when it comes to speculation, "the unicorns did it" is just as meaningful as anything else...
Start with:
\vec m = \frac{1}2 \int \vec r \times \vec J(\vec r) d^3\vec r
If the current is confined to a single planar wire:
\vec J(\vec r) = I δ(z) δ(\vec r-\vec r' )
which leads to:
\vec m = \frac{I}2 \int \vec r' \times \vec d r'
\vec m = \hat{z}\frac{I}2 \int r' sin γ d...
Where the wire joins and leaves the coil is arbitrary, as long as as you have one continual coil (no cut anywhere breaking the circuit) and each coil loop turns the same way around the core. The current that adds the most to the magnetic field is the current through each loop in the coil, not...
Yes, if it is changing. It's called Faraday's law of induction. This is the basic operating principle behind electric generators. As tiny-tim mentioned, the electric field and magnetic field are really different faces of the same thing. If you move a wire near a magnet, the magnetic field exerts...
If I am standing motionless on the surface of the earth, then my frame IS the earth's frame (as long as we choose the same origin). The act of standing on the earth and my feet being motionless compared to the ground means that I am rotating at the same speed as the earth. We are both therefore...
No, the force is the product of both masses, and they both feel the same force (action and reaction forces equals). Think of F = m a for the apple the for the earth, where F is the same for both. For the earth, m is huge, so the acceleration a must be tiny to keep F constant and equal to the F...
No. A reference frame that is stationary relative to the earth's ground is non-inertial because the earth is rotating. The rotation of the earth has nothing to do with the sun or stars. It is rotating about its own axis. An inertial frame is more than a frame that is stationary relative to...
Evanescent waves are non-traveling, spatially exponentially decaying waves. They are real, but do not carry energy directly. Think of wiggling a rope trying to get a wave to go down it but the rope is so heavy that you never succeed in getting a wave to travel down, you only get a fixed wiggle...
From Wikipedia:
"In taller plants and trees however, the force of gravity can only be overcome by the decrease in hydrostatic (water) pressure in the upper parts of the plants due to the diffusion of water out of stomata into the atmosphere"
The way that index of refraction depends on frequency is very complicated and material dependent. There is not a single simple equation to describe it. It has to do with resonant frequencies of the material which depends on the material's atomic composition as well as lattice structure. The...
You can think of it as one monochromatic wave with a horizontal polarization and traveling in the z direction added non-coherently to another monochromatic wave with a vertical polarization traveling in the z direction. Non-coherently in this case means that there is a random phase difference...
When you switch on current through a coil, even if it is a DC current, you are going from 0 current to a non-zero current. This is a changing current. Changing currents radiate electromagnetic waves. The wavefront travels out away from the coil at the speed of light. You should be googling terms...