Are you sure Earnshaw's Theorem applies here? It simply states that an electrostatic trap is impossible. This theorem is a result of Possoin's Equation in an area of zero charge. Which reduces it to Laplace's Equation. Functions satisfying Laplace's Equation admit no maxima or minima and you...
I am not sure what you are driving at when you say "it just works out".
It is not a difficult matter to prove the equivalance of Newtonian and lagrangian dynamics. You can find this proof in just about all undergraduate classical mechanics texts, see Marion. Given this proof, it doesn't just...
That's a good question. In the merry go round analog, as soon as you loose your grip then no force is left to fight the centrifugal force and you will definitely fly off. However, in the Earth example once you loose your "grip" gravity is still fighting to pull you back down to the earth. So...
In this context, the contact force is F=mg where F is the force that some object of mass m feels due to gravity g.
g is an acceleration and equals 9.8m/s^2 at sea level.
An important point to keep in mind though is that g=9.8 is actually the effective gravity. Meaning it is the acceleration...
When you rotate on a merry go round a "force" tries to throw you off right? Why don't you get thrown off? Because you are holding on to something or the friction between you and the merry go round keep you there, ie: some counter force is applied to keep you in place.
Now recast this:
When you...
This is both true and a good point. However, technically this statement is not the converse of the uniqueness theorem (though the techincality is extremely trivial.)
There are actually two statements:
First Uniqueness Theorem: The potential in a volume V is uniquely determined if the...
So you want to know if the following is true:
If you know the potential, electric field, then you know the charge distribution.
I would say the converse is not true. Afterall, we use the method of images to calculate the potential based on a ficticious distribution of charge.
That makes sense, thanks cesium that was the kind of explanation I was after.
So Taylor expand just two of the above terms (one from each face) and look at those to see how the forces work out?
I have a general equation for the potential at any point inside the cube but it is really ugly:
\frac{q}{4\pi\epsilon_{0}}\sum{\frac{1}{r_i}}
where
r_i=\sqrt{(a+x)^{2}+(a+y)^{2}+(a+z)^{2}} ; 1 \leq i \leq 8
and the sign ordering preceding the x, y, and z is different for each r
ie: +++...
I just came across Earnshaw's Theorem which states:
A charged particle cannot be held in stable equilibrium by electrostatic forces alone.
As an example it said that equal and fixed point charges at the corners of a cube could not hold stationary a point charge at the center.
There was...
Easy with the big vocabulary, maybe tomorrow you can help me learn my farm animals. (Kidding of course.):tongue2:
When I first noticed this effect it was with two fences. However, since then I have observed it for only one fence. You have to be moving pretty fast though (or atleast I think)...
This makes good sense. It is the same reason (CRT) computer screens bobble up and down when viewed on a TV (such as while watching the news). However, I could have sworn that I've seen this in real life. Maybe my mind is playing tricks on me...
How does color or polarization separation...
So I have two (somewhat) related questions.
1) Why is it wheel rims (or spokes) sometimes appear to spin backward? Everytime I see this it drives me crazy. I just cannot figure out how a wheel spinning real fast in one direction appears to be spinning real slow in the other direction.
2)...