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What is electric charge, and how strong is the force between two charged objects?

Topic 10.1 Electric Charge and Coulomb's Law: describe electric charge and apply Coulomb's law to the force between point charges.

A focused answer to AP Physics 2 Topic 10.1, covering the two kinds of electric charge, the attraction and repulsion rule, the quantisation and conservation of charge, and Coulomb's law for the inverse-square force between point charges, with full worked examples.

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  1. What this topic is asking
  2. What electric charge is
  3. Coulomb's law
  4. Direction and superposition
  5. Try this

What this topic is asking

The College Board (Topic 10.1) wants you to describe electric charge, its two kinds and the rules of attraction and repulsion, and to apply Coulomb's law for the force between point charges, recognizing it as an inverse-square law.

What electric charge is

Charge is carried by the constituents of atoms: protons are positive, electrons negative, and a neutral object simply has equal numbers of each. Objects become charged by transferring electrons, not protons, which is why charging is always a redistribution of existing charge, never creation. Two principles govern it: conservation (the total charge never changes) and quantisation (charge comes in whole multiples of ee). When identical conductors touch, they share their total charge equally, a frequent exam scenario.

Coulomb's law

Coulomb's law is the foundation of electrostatics. Its structure mirrors Newton's law of gravitation: a product of the two sources divided by the square of the distance. The differences are that charge comes in two signs (so the force can attract or repel, unlike gravity which only attracts) and that the electric force is vastly stronger. The inverse-square dependence is the most-tested feature: tripling the separation cuts the force to one ninth, and halving it quadruples the force.

Direction and superposition

Coulomb's law gives a magnitude; the direction comes from the signs. Draw the force on each charge along the line connecting them, pointing toward the other charge if they attract (opposite signs) and away if they repel (like signs). When more than two charges are present, the net force on any one is the vector sum of the Coulomb forces from each of the others (the principle of superposition): compute each pairwise force separately, then add the vectors. This component-by-component addition is exactly the vector toolkit from mechanics applied to charges. The strategic point of this topic is that Coulomb's law is the source of everything in the unit: the electric field (Topic 10.3) is just this force per unit charge, the electric potential energy (Topic 10.4) is the work stored in assembling charges against this force, and circuits (Unit 11) move charge that this force sets in motion. Mastering the inverse-square reasoning and the sign rule here pays off across all of electromagnetism.

Try this

Q1. State the rule for whether two charges attract or repel. [1 point]

  • Cue. Like charges (same sign) repel; unlike charges (opposite signs) attract.

Q2. Two charges exert a force of 8.08.0 N on each other. State the force if the distance between them is tripled. [1 point]

  • Cue. One ninth, so 0.890.89 N (inverse-square: 32=93^2 = 9).

Exam-style practice questions

Practice questions written in the style of College Board exam questions on this dot point, with worked answer explainers. The year tag is the paper they imitate, not the source.

AP 2024 (style)6 marksSection II (short FRQ). Two small charged spheres are 0.300.30 m apart. Sphere A carries +4.0+4.0 microcoulombs and sphere B carries −2.0-2.0 microcoulombs. Take k=8.99×109k = 8.99 \times 10^9 N m squared per C squared. (a) Calculate the magnitude of the electric force between them. (b) State whether the force is attractive or repulsive and justify it. (c) State and justify how the force changes if the separation is doubled.
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A 6-point FRQ on Coulomb's law.

(a) Magnitude (3 points): F=k∣q1∣∣q2∣r2=(8.99×109)(4.0×10−6)(2.0×10−6)(0.30)2=0.07190.09=0.799F = \dfrac{k|q_1||q_2|}{r^2} = \dfrac{(8.99 \times 10^9)(4.0 \times 10^{-6})(2.0 \times 10^{-6})}{(0.30)^2} = \dfrac{0.0719}{0.09} = 0.799 N.
(b) Direction (2 points): the charges have opposite signs, so the force is attractive (unlike charges attract).
(c) Doubling the distance (1 point): the force follows an inverse-square law, so doubling rr reduces the force to one quarter, 0.200.20 N.

Markers reward the Coulomb's law calculation, the attractive direction for unlike charges, and the inverse-square reasoning.

AP 2023 (style)1 marksSection I (multiple choice). Two identical metal spheres carry charges of +6q+6q and −2q-2q. They are touched together and then separated. What charge does each carry afterward? (A) +6q+6q and −2q-2q (B) +2q+2q each (C) +4q+4q each (D) zero each. Justify your reasoning.
Show worked answer →

A 1-point MCQ on conservation and sharing of charge. The answer is (B).

Charge is conserved, so the total +6q+(−2q)=+4q+6q + (-2q) = +4q is unchanged. Identical spheres in contact share the total charge equally, so each carries +2q+2q. The trap is (C): the total to share is +4q+4q, and split between two spheres each gets +2q+2q, not +4q+4q.

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