Electric charge & electric fields
The idea
Charge is to electricity what mass is to gravity: the property that lets objects exert the force. It comes in two signs — like charges repel, opposites attract — and is measured in coulombs (C), carried in tiny lumps by electrons (negative) and protons (positive). Charge is conserved: rubbing a balloon on hair does not create charge, it just transfers electrons from one surface to the other. Coulomb's law gives the force between point charges: F = kq₁q₂/r², with k = 8.99 × 10⁹ N·m²/C².
The structure should look familiar — it is an inverse-square law like gravitation, but staggeringly stronger and able to repel as well as attract. The electric field extends the idea: a charge fills the space around it with a field E, defined as the force per coulomb that a small positive test charge would feel, so E = F/q and a point charge produces E = kq/r². Field lines point away from positive charge and into negative charge, and their crowding shows field strength.
A persistent misconception is that the field is only there when something feels it. The field exists whether or not a test charge is present — it is the middleman that carries the interaction, and it is the more fundamental object: first the charge creates the field everywhere, then the field pushes on whatever charge shows up.
Worked example
A +3.0 μC charge and a −2.0 μC charge are held 0.50 m apart. Find the magnitude and direction of the force between them, and the strength of the electric field the +3.0 μC charge creates at the location of the other charge.
- Identify the interaction: the charges have opposite signs, so the force on each is attractive — each charge is pulled straight toward the other with the same magnitude, by Newton's third law.
- Convert to SI units before computing: 3.0 μC = 3.0 × 10⁻⁶ C and 2.0 μC = 2.0 × 10⁻⁶ C.
- Apply Coulomb's law with magnitudes: F = kq₁q₂/r² = 8.99 × 10⁹ × (3.0 × 10⁻⁶ × 2.0 × 10⁻⁶)/0.50².
- Work the arithmetic: the numerator product is 8.99 × 10⁹ × 6.0 × 10⁻¹² = 0.0539 N·m², and dividing by 0.25 m² gives F ≈ 0.22 N.
- For the field, use only the source charge: E = kq/r² = 8.99 × 10⁹ × 3.0 × 10⁻⁶/0.25 ≈ 1.1 × 10⁵ N/C, pointing away from the positive source.
- Cross-check the two answers: the force should equal field times the charge placed in it, and 1.08 × 10⁵ × 2.0 × 10⁻⁶ ≈ 0.22 N — the ledger agrees.
Answer. The charges attract with a force of about 0.22 N, and the +3.0 μC charge creates a field of about 1.1 × 10⁵ N/C at the other charge's location.
Check your understanding
- Why does dividing the force by the test charge give a quantity that describes the source charge's influence alone?
- How are Coulomb's law and Newton's law of gravitation alike, and what are the two deepest ways they differ?
- What happens to the force between two charges if both charges are doubled and the separation is also doubled?
- How would you explain to a friend where the charge comes from when a rubbed balloon sticks to a wall?
Build the foundations first
Electric charge & electric fields builds on these concepts. If any feel shaky, start there.