Calculating Electric Potential from a Charge Distribution · seed 1 · A4, ink-friendly. The answer key prints on its own page for grown-ups.

Voltage adds like numbers

Science · Electricity & Magnetism · ages 18-19
Name ______________________   Date ____________

  1. A positive charge released in a field moves from high potential toward low potential.

    Circle one:   True   False

  2. What is electric potential?

    • Potential energy per unit charge
    • Force per unit mass
    • Charge per unit time

  3. What is the potential of a point charge q at distance r?

    • k times q over r squared
    • k times q over r
    • k times q times r

  4. Why is the potential integral of a charged ring easier than its field integral?

    • It uses no integral at all
    • It ignores half the charge
    • It adds numbers with no direction bookkeeping

  5. Four different corner charges surround a square center. How do you get the potential there?

    • Add the four k times q over r numbers
    • Add the four field arrows tip to tail
    • Take only the largest corner charge

  6. Where should you place zero potential?

    • Only at the positive terminal
    • Wherever convenient, often at infinity or ground
    • Zero can never be chosen freely

  7. Two students solve one problem, one with zero at infinity and one with zero at ground. Why do both get the same motion?

    • Only potential differences move charges, so the shared reference drops out
    • Ground zero always gives larger answers
    • Infinity zero is the only legal choice

  8. Potential falls steeply along x at some point. What is the x component of the field there?

    • Zero, since potential is not a vector
    • Large, pointing toward falling potential
    • Large, pointing toward rising potential
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Answer key

For grown-ups. Fold this page away before handing over the rest.

Voltage adds like numbers W1-mt_B4WiVkpH4j-s1

  1. True · It rolls downhill in potential, turning stored energy into motion.
  2. Potential energy per unit charge · Dividing stored energy by charge gives a quantity independent of the test charge.
  3. k times q over r · Potential fades as one over r, while the field fades as one over r squared.
  4. It adds numbers with no direction bookkeeping · No arrows means no cancelling components to track before summing.
  5. Add the four k times q over r numbers · Potential is a scalar, so the four contributions add as plain numbers.
  6. Wherever convenient, often at infinity or ground · Only differences move charges, so the reference level is free.
  7. Only potential differences move charges, so the shared reference drops out · Shifting every potential by a constant leaves all differences unchanged.
  8. Large, pointing toward falling potential · Field components equal minus the slope of V, so steep falls mean strong fields downhill.
Worksheet · LightMySky