Potential of Point Charges and Superposition

The electric field at a point is a vector: each charge contributes an arrow with a direction, and you add those arrows tip to tail, worrying about angles and components. Potential has no direction. Each charge contributes a plain signed number, kq/r, and you just add the numbers. A positive charge contributes a positive number, a negative charge contributes a negative number, and the sum is whatever arithmetic gives you. That's the whole trick: potential trades geometry for bookkeeping.

To find the potential at some point from several charges, measure the straight-line distance from each charge to that point, compute kq/r for each one keeping the sign of q, and add all the results. There's no projection, no resolving into x and y pieces, because a scalar has no components. If four charges sit at the corners of a square and you want the potential at the center, you just need four equal distances and four signed charges — add kq/r four times.

This is why potential problems feel easier than field problems even though both start from the same point-charge source. It also sets up the next move in the unit: once you have potential as a function of position, you can recover the field by taking its negative gradient, E = -dV/dr. So this topic is the arithmetic half of a two-step pattern — sum scalars to get V, then differentiate to get the vector field back — and it also lets you find where V = 0, which is generally a different location from where E = 0.