---
title: "Calculating Electric Potential from a Charge Distribution"
description: "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."
canonical: https://lightmysky.com/learn/science/calculating-electric-potential-from-a-charge-distribution-mt_B4WiVkpH4j
source: https://lightmysky.com/learn/science/calculating-electric-potential-from-a-charge-distribution-mt_B4WiVkpH4j.md
retrieved: 2026-09-12
---

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# 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.

Subject: Science · Area: Electricity & Magnetism · Ages 18 to 19
Page: https://lightmysky.com/learn/science/calculating-electric-potential-from-a-charge-distribution-mt_B4WiVkpH4j

## Ready when they can

- 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

## Lesson: Voltage adds like numbers

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.

**Example.** 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.

**Tip.** 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.

**Recap.** Potential adds as numbers, zero sits where you choose, and field points down its slope.

## Practice

8 questions on this page, each with its working shown.

## Needs first

- [Conductors, Shielding and Surface Charge](https://lightmysky.com/learn/science/conductors-shielding-and-surface-charge-mt_2zmzTE-dgL)
- [Electric Potential and the Uniform Field Between Plates](https://lightmysky.com/learn/science/electric-potential-and-the-uniform-field-between-plates-mt_LKTfeYxNde)

## Opens up

- [Gauge Freedom and the Potentials as the Working Variables](https://lightmysky.com/learn/science/gauge-freedom-and-the-potentials-as-the-working-variables-mt_BovDzq3WZm)
- [Recovering the Field from the Potential Gradient](https://lightmysky.com/learn/science/recovering-the-field-from-the-potential-gradient-mt_EqCLB9bqG1)