Calculating Electric Potential from a Charge Distribution
Potential is a scalar, so contributions add without any concern for direction, which usually makes it easier to compute than the field. For a continuous body it is again an integral over the charge.
What a learner can do afterwards
- Adds the potentials of several point charges at a given place
- Sets up and evaluates the potential integral for a line or ring of charge
- Explains why the choice of zero potential is free and where it is normally put
1 · Read
Electric potential is potential energy per unit charge, measured in volts. One volt is one joule per coulomb. A positive charge rolls from high potential to low the way a ball rolls downhill, trading stored energy for motion.
Potential is a plain number with no direction, so contributions simply add. A point charge gives k times q over r, with zero set at infinity far away. For a square with a different charge at each corner, add the four numbers at the center and you are done.
A continuous body is handled the same way as the field, except the sum is scalar. Chop it into tiny charge pieces, add k times each piece over its distance, and never wrestle with arrows. That is why potential integrals are usually easier than field integrals.
Only differences of potential matter, so put zero wherever it helps: at infinity, at ground, or at one terminal. The field points down the steepest fall of potential, with each component equal to minus the slope of V along that direction.
Potential adds as numbers, zero sits where you choose, and field points down its slope.
2 · Watch
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Where it sits
8 questions wait behind this lesson, each with its answer explained. Every answer feeds the sky: stars light as they are learned, and dim when it is time to come back.