These don't carry the explanation I'm looking for.
Why doesn't the positive test charge (cat, here) experience an attraction to the wire if the electrons are getting length contracted?
(1) https://www.youtube.com/results?search_query=relativity+and+electromagnetism
(2)
If I understand this correctly, then, well, shouldn't all current-carrying wires exhibit a small amount of positive charge?
Net charge is still zero for the circuit before and after.
It's just the potential difference caused by the charge separation on C1 that leads to the different Qs you see in the end state?
So, it may seem like we went from 48mL excess to 64mL excess and violated conservation of mass.
But, in reality, the water is in the pipes as well? Just at a different pressure?
There's some misconception I have that's causing the math to not add up:
LH: 48mL -> 32mL (-16mL)
RH: 0mL -> 32mL...
+Q will accumulate on one side, -Q on the other.
Net charge will be zero.
Let's say I have two capacitors in series.
If I am asked what the total charge accumulated on any 1 plate on both capacitors is, what would the answer be?
Q+Q = 2Q?
Q of the equivalent combined capacitor = Q on any of the...
There must be something I'm not understanding about capacitors in series.
I know that we can treat them as one equivalent capacitor with:
(1) with 1/Ceq,
(2) same Q as anyone of the capacitors,
(3) and add up the Vs for the sum total V across them.
If the equivalent capacitor (Ceq) would...
The professor wants what Paul's Online Notes shows.
Directly substitute all variables and differential symbols ("dx" and "du").
Constants, you can divide.
I have come to agree with his method.
The division thing, except in the case of a constant, seems to be a mathematical coincident/fluke?
Homework Statement:: I need to develop my instincts on when to use u-sub, integration-by-parts, trig substitution, etc. But, I need to read/see tons of problems actually being solved with these techniques to know which technique to apply quickly.
Relevant Equations:: Sorry for the vague...
Understood.
As a conclusion, I think this is the best way for a student to proceed/process u-substitution:
Manage constants by "division" / "adjustment" BUT directly replace all other variables.
It makes intuitive sense to me.
But, if g'(x) = 0, then the original g(x) within f(x) would be a constant, which would make f(x) a constant. This, in turn, would change our entire approach to the integral and perhaps even obviate u-substitution.