*Serious* Questions about Voltage / PE

[kaotak]

Okay, I'll pose some serious questions.

1) What does the voltage due to a point charge really mean? I know that the voltage due to a point charge can be found by V = kq/r, but what does this mean, why is it useful to know? If you know the voltage at an arbitrary point, what does that really tell you?
2) What does the voltage of a Van de Graaff generator mean? Across what distance does it span?
3) My textbook (Physics for Scientists and Engineers) said that the potential energy of a pair of point charges separated by a distance r is the work it took to bring those charges from infinite separation to the separation r. Question: How can one unlock that potential energy that comes from the work invested in moving the point charges? For instance, one can unlock the potential energy of height by jumping off a cliff. How do you do it for a pair of point charges? What "falls" and where does it "fall"?
4) Why are voltage drops useful? What happens when you run a current through them? How do we get energy from voltage drops?
5) In circuits, why are there voltage drops along the resistors? What causes the voltage to be higher at a point before the resistor than at a point after the resistor?

 

[interested_learner]

1) To quote from Schaum's Outline in EM (page 60):

"The potential (ie voltage) of point A with respect to point B is defined as the work done in moving a unit charge Q from B to A."

In other words voltage is potential energy. It is exactly like a ball that you raise off the surface of the Earth. The higher you go the greater the potential energy. So voltage HAS to be defined in reference to something.

2) It is usually defined in reference to infinity.

3) The energy is unlocked as the particles far toward each other. This increases their momentum.

4) The same way gravitational drops are useful. The water dropping from a dam creates a lot of energy. Of course how much is dependent on the current also. The voltage is like the height of the dam and the electrical current is like the water current. (Not exactly but it is a useful analogy).

5) As the electrons move through the resistor they convert their energy to heat. That energy has to come from somewhere and that is the voltage drop.

 

[kaotak]

Okay, thanks for the answers, they're pretty good =p

Some things I realized during this that really helped:

A) In a waterfall, the water comes from somewhere, a more flat stretch. But how does it move along a flat stretch? It doesn't, there's a small degree of imperfection in it, the stretch is slightly downhill. This allows the water to move along a river bank and then reach the waterfall. It's the same with currents in wire. The wire has a SLIGHT amount of resistance, causing a slight voltage drop, which allows the current to move to the resistors. Then when they get to the resistors, they lose energy to heat, causing a voltage drop as you said like a waterfall.

B) I thought that voltage being defined as the work of moving a test charge from point A to point B means that we had to provide the work and it couldn't be useful. But an electric field could be providing the work, just like a gravitational field, which makes it useful and can ultimately give charged objects kinetic energy as it accelerates them.

 

[kaotak]

By the way... this is not homework. These are questions that I came up with...