Recent content by Mike Pemulis

Yup, a sphere between the orbits. If I had to guess, I would say a ring would work too, but I'm not positive. A sphere would definitely work.

That wouldn't work, right? An third planet might disturb the second planet's orbit, deforming it away from a perfect circle, but it wouldn't really make it go faster. And that's what we need to explain. Let's try again. We need to explain why the outer planet orbits faster than we would...

Yes, but you had the right idea. Read the article again and think.

Looks good to me. Why do you think that's wrong? I'm assuming you're not making a simple mistake like confusing degrees and radians.

I'll just leave this here.

I'm not sure about (a). I've taken some QM, and it seems like that expression is way too general to be simplified usefully. The only thing I can think of is that we can always write an operator as, A = \sum_{a'} a' | a' \rangle \langle a' | Where a' is an eigenvalue and |a' \rangle is the...

I don't know then. Would you mind typing out the problem exactly as it is stated?

Try multiplying by 25 percent instead. 75% efficient means that 25% of the applied work is converted to heat.

I can't see the diagram -- the site you linked to asks for a login name and password. Can you copy the diagram to imgur or something so we can see it? However, I am familiar with this type of problem, so I can give some pointers so maybe you can do it yourself. 0. You probably need Ohm's...

Sorry to be blunt, but that is like reading about the history of classical music without knowing how to read sheet music or play an instrument. You might read about different composers and their music, but you couldn't get a real understanding of what they were doing. I recommend you pick up a...

I've never studied quaternions, actually, and it looks like I'm not as knowledgeable about the history of E&M as you. But my understanding is that all these different formulations lead to exactly the same physical predictions, although as IsometricPion notes, some formulations are more...

Yes, but that's not what Whittaker did. He writes the E and B fields (not just the B field) in terms of a more complicated differential operator (not the gradient) of two different scalar functions. To see how this is possible, read the paper!

It doesn't work that way. The electric and magnetic fields exist at all points in space, just as they always did. Whittaker is saying that you can write the six total components in terms of derivatives of only two scalar fields. It is the same as saying that the electrostatic field can be...

The phase shift problem is due to the multivalued-ness of the arctan "function" -- there are many angles that give the same tangent, even within the same 2π "period." In particular, for every solution in the first quadrant there is one in the third, and for every solution in the second quadrant...

Nice find! Yeah, it is possible to do this; Whittaker is correct. I think a good birds-eye-view explanation for why this is possible is that the differential form of Maxwell's Equations for electric and magnetic fields are four equations involving two vectors with three components each. This...