Recent content by Dale

So that formula doesn’t really apply. There are no solitary point charges in that circuit. There is a continuous distribution of surface charge along all the conductors. That distribution doesn’t have a nice closed form expression.

Is that formula supposed to be the voltage at a point or the voltage due to a point charge? Read the surrounding text carefully

It is more that net work is different from total work. The net work is the net force times the displacement of the center of mass. That is equal to the change in KE. The work of an individual force is the individual force times the displacement of the material at the point of application of...

This actually is not the case. The net work being zero just means that the KE did not change. It does not imply that any other forms of energy are unchanged.

Oh, right. It isn’t quite a central potential because the force depends on the second derivative of the radial coordinate.

This would be a central force with a ##r^0## force instead of the usual ##r^{-2}## force https://en.m.wikipedia.org/wiki/Classical_central-force_problem

Symmetries in spacetime are given by Killing vector fields. These are standard GR vectors, so they are covariant. They reflect the underlying geometry and are independent of any coordinate system or observer. The basic premise here is flawed. If the spacetime is spherically symmetric then it...

The direction of the field is not a real direction. The direction of the magnetic field is a convention, specifically the right hand rule. There is already a convention in the direction the current flows. This is a different convention, specifically the convention that the proton is positively...

It is clockwise because most people are right handed so clockwise follows a right hand rule. If most people were left handed we could have used a left handed rule and the physics would be fine. A left hand rule would make it counter clockwise

Forget the cameras for now. Focus on the clocks. When Spock is on Mars then $$c^2 d\tau_{spock}^2=c^2 dt_{mars}^2-dx_{mars}^2\bigg|_{spock}$$$$\left(\frac{d\tau_{spock}}{dt_{mars} }\right)^2=1-\left(\frac{dx_{mars}}{c \ dt_{mars}}\right)^2 \bigg|_{spock}=1$$ and $$c^2 d\tau_{spock}^2=c^2...

Oh so much is wrong. You really should study some of the basics. If you actually work through the real math here there are no conflicts. First, a notation like ##d\tau_{ship}/d\tau_{mars}## makes no sense. Two clocks moving with respect to each other are only co-located at one event. Comparing...

When someone is thinking about pressure “acting in a direction” what they are actually thinking about is a quantity called the stress. Stress is a tensor so it maps a vector to a vector. In this case an infinitesimal area is represented by a vector perpendicular to the area, and the stress...

Yes. Is there some reason that isn’t clear to you?

It is possible, and abundant evidence shows that is in fact the way the world works. However the numbers you made up above aren’t matching your words. When you are talking about the rate of Spock’s clock the appropriate quantity is not ##t_{spock}## but ##d\tau_{spock}/dt_{ship}## etc...

Ok, there is your problem. ##t_{spock}=t_{mars}## is true, but none of your inequalities are true. By the Lorentz transform $$t_{mars}= \frac{1}{\sqrt{1-v^2/c^2}} \left(t_{ship}-\frac{v\ x_{ship}}{c^2}\right)$$ Whether this is greater than or less than ##t_{ship}## depends on ##x_{ship}##...