Electric Charge and Electric Force
Electric charge is signed and quantized; Coulomb’s law gives the magnitude and direction of the electrostatic force between pointlike charged objects, with vector superposition for several sources.
Electric Charge and Electric Force: quick answer
Electric charge is signed and quantized; Coulomb’s law gives the magnitude and direction of the electrostatic force between pointlike charged objects, with vector superposition for several sources. Electric-force problems are mainly model and vector problems. First decide whether each object can be treated as a point charge, then determine attraction or repulsion, calculate each pairwise magnitude, and only then add force vectors. The same interaction also illustrates why ordinary contact forces ultimately arise from electromagnetic interactions.
Limit direct electric-force calculations to four or fewer interacting charged objects unless the arrangement has high symmetry; use the point-charge approximation only when object size is negligible for the geometry.
What you should be able to explain and do
Use these as closed-note retrieval prompts before looking at the worked examples.
Distinguish charge sign, magnitude and quantization.
Use Coulomb’s inverse-square law with the correct medium permittivity.
Determine force direction from charge signs before calculating magnitude.
Compare electrostatic and gravitational interactions and use vector superposition for several charges.
Key terms you need for this lesson
Definitions stay beside the model so a reader never has to leave the lesson to understand a prerequisite term.
elementary charge
elementary charge is the magnitude e=1.60×10⁻¹⁹ C carried by a proton and the magnitude of the charge carried by an electron.
electrostatic force
electrostatic force is the attraction or repulsion between charged objects when the charge distribution can be treated as stationary.
point-charge model
point-charge model is an approximation that ignores an object’s physical size compared with the relevant separations.
permittivity
permittivity is a property of the medium that measures its electric polarization response and therefore affects electrostatic interaction strength.
conductor
conductor is a material whose mobile charge carriers can redistribute readily.
insulator
insulator is a material in which charge carriers do not move freely through the material.
Know what each relationship means and when it applies
The equation, variables, vector/scalar nature, model condition and physical anchor belong together.
| Relationship / model | Variables & units | When to use it | Physical anchor |
|---|---|---|---|
F_E = |q₁q₂|/(4πεr²) | F_E electric-force magnitude (N); q₁,q₂ charges (C); ε permittivity of the medium (F/m); r center-to-center separation (m). In vacuum, 1/(4πε₀)=k_e≈8.99×10⁹ N·m²/C². | point charges or spherically symmetric charged objects when the point-charge model is valid | If the separation doubles while charges and medium stay fixed, the force magnitude becomes one fourth as large. |
q = ne | q net charge (C); n an integer counting excess or missing elementary charges; e=1.60×10⁻¹⁹ C | ordinary charge quantization | An object with 5×10⁶ excess electrons has q=−5×10⁶e. |
F_net = vector sum of F_i | F_net net electrostatic force vector (N); F_i individual force vectors from the other charged objects | two to four interacting charges, or a higher-symmetry case | For three charges, determine each force direction first and add components rather than adding magnitudes. |
What a strong diagram or graph must show
Translate the same physical model across words, diagrams, graphs and equations.
Free-body diagram
show electric force separately from weight, tension, normal force or other interactions.
Charge-line diagram
mark signs and center-to-center separations before calculating.
Vector components
choose axes and add x/y components when forces are not collinear.
Force-versus-distance graph
inverse-square behavior is curved; F versus 1/r² is linear when charges and medium are fixed.
Change the model and inspect what must respond
Make a prediction first. Then move one control and explain the output using the governing relationship and representation.
Coulomb force + inverse-square explorer
Change both charges and their separation. Predict attraction/repulsion and the factor change before reading the result.
Two examples with the model choice shown
The goal is to expose the reasoning pathway, not only the final number.
Inverse-square comparison
Situation: Two point charges exert a 3.6 N force at separation r. The separation becomes 3r while charges and medium stay unchanged.
Reasoning: Coulomb force is proportional to 1/r². Increasing r by 3 changes the magnitude by 1/3².
The new force magnitude is 3.6/9 = 0.40 N; attraction or repulsion is unchanged because the charge signs did not change.
Suspended charged spheres
Situation: Two small charged spheres hang from the same support. Sphere A’s string makes a larger angle from vertical than sphere B’s.
Reasoning: By Newton’s third law the electric forces on A and B have equal magnitude. A larger angle therefore cannot be explained by a larger electric interaction on A; compare the weights/masses using the force triangles.
The angle difference is evidence that the gravitational force (and therefore mass) differs, not that the pairwise electric-force magnitudes differ.
Recognize the physics before reaching for an equation
Use the cue to choose the model, connect it to nearby ideas, then reject any method whose assumptions do not match the situation.
What should trigger Topic 10.1?
Use Coulomb-force reasoning when discrete charged objects interact and the question asks for force magnitude, direction, or inverse-square scaling.
How this idea fits the course
Topic 10.3 converts source-charge interactions into the field model; 10.4 reframes the same interaction using potential energy.
Scope check before solving
Limit direct electric-force calculations to four or fewer interacting charged objects unless the arrangement has high symmetry; use the point-charge approximation only when object size is negligible for the geometry.
Turn this topic into measurable evidence
A strong investigation identifies variables, controls competing causes, repeats trials and chooses a graph from the predicted functional dependence.
Investigation target
Use force-versus-separation data or simulation to test an inverse-square model.
Reasoning errors to eliminate
Repair the physical model before doing more arithmetic.
Six things you should be able to do before moving on
Use these as closed-note transfer prompts.
- I can define the core quantities and state whether each is vector or scalar.
- I can choose the governing relationship only after identifying source, probe and system boundary.
- I can explain every variable, unit, sign and reference convention.
- I can translate the situation into a field/equipotential/energy/geometry representation.
- I can predict direction or factor change before calculating.
- I can design or critique an experiment and justify a claim with data or physical principles.
Practice is kept on its dedicated pages
Finish the lesson first. Then open the separate topic bank when you want exam-style practice without replacing the teaching content above.
42 multiple-choice questions
Use the exact-topic MCQ bank to test model selection, representations, calculations and boundaries after learning the concept.
Open 42 Topic MCQs4 multipart free-response tasks
Use the exact-topic FRQ set for mathematical, representation, experimental and qualitative/quantitative reasoning.
Open 4 Topic FRQsTopic 10.1 FAQs
What makes charge positive or negative?
The sign describes the type of electric charge. Protons carry +e, electrons −e and neutrons have zero net electric charge.
Why is Coulomb force an inverse-square law?
For pointlike sources in three-dimensional space, the field/interaction strength spreads geometrically so the magnitude varies as 1/r².
Are electric forces always stronger than gravity?
For typical charged particles the electrostatic interaction is enormously stronger, but large macroscopic systems are usually nearly neutral, allowing gravity to dominate at astronomical scales.
Can an electric force be attractive and repulsive?
Yes. Like signs repel and opposite signs attract.
How many charges should I calculate directly?
Keep direct multi-charge calculations to four or fewer sources unless symmetry makes a larger arrangement simple.
What does permittivity mean physically?
It describes how strongly a medium polarizes in response to an electric field; that response changes the effective electric interaction within the material.