Recent content by haruspex

I could well be wrong, but to me they read as independent questions. In q2, the two subsystems are in thermal equilibrium with each other. That means the energy of each is in proportion to its number of particles. Since they have two particles each, each subsystem has energy 3e. In q3, we...

Yes.

Looks to me to be the same logic as in https://www.physicsforums.com/threads/derivation-of-induced-charge-on-a-dielectric.846504, but run in the opposite direction.

That would be most helpful.

Because until post #16 the relationship between posts #1 and #7 was not apparent. How to prove the formula in post #7 depends what your starting point is, i.e. how k is defined. I don't mean merely that it is the dielectric constant; what does it mean in terms something physically observable...

I doubt that will help. It is a matter of interpretation of the question. As I read it, the two subsystems have come into equilibrium with each other, so now have the same total energy. This should increase the number of microstates somewhat, that representing an increase in entropy, but not...

I don't think that is what is meant. It further explains "after being allowed to exchange heat and energy". What have exchanged heat and energy, and what have been brought into equilibrium as a result?

What do you think two subsystems that have reached thermal equilibrium means for the total energy of each subsystem?

Please clarify the relationship between posts #1 and #7. What happened to 1-1/k and induction? Should we ignore post #1?

The force would correspond to ##\tan(\theta)## rather than to ##\sin(\theta)##, but I assume the angles were small. Please show your working for the equation you got.

That was in post #7, but I don’t get how this relates to post #1.

Belatedly, I realised the logic behind going for as much tangential force as possible is that it maximises the immediate rate of gain of total energy. Whether that also maximises the long term rate of gain is unclear, but it is a reasonable starting point. So I changed my model to adjust the...

I think the situation is more complicated than that. For a dielectric plane lamina, the field is diminished within the lamina but there is no external consequence. I believe we can think of that situation as equivalent to an induced charge on each surface. Since those charges are equal and...

How can you tell it is too stiff? Maybe option 2 is too soft. The question seems to require some ergonomic or comparison data, such as the modulus of some common item you can relate to.

I don’t understand what k is. It makes the medium sound more like a dielectric than a conductor.