Physics › ⚡ Electricity & Magnetism

Electric Charge & Fields

The invisible push and pull that starts with a rubbed balloon and ends with Coulomb's law.

High schoolAP Physics 2 level
Electric Charge & Fields — illustration
Illustrative hero image.
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The big idea: Every electric effect — static cling, lightning, the pull between charges — comes down to one thing: like charges repel, opposite charges attract, and that force follows a precise inverse-square rule. Once you can calculate the force with Coulomb's law and describe the space around a charge with the electric field, you can predict how any charged object will behave before it even moves.
🎯 By the end, you'll be able to
  • Explain what electric charge is and describe how conductors and insulators handle it differently
  • Calculate the electrostatic force between two point charges using Coulomb's law
  • Define electric field, calculate it from F=qE or from a source charge, and connect it back to force
  • Read a field-line diagram to predict the direction and relative strength of the field at any point
📎 You should already know
  • Newton's Laws of Motion (force, in general)
  • Working with scientific notation and exponents
  • Basic vector direction (attraction vs. repulsion)

Why does your hair stick to a balloon?

Rub a balloon on your hair and something invisible happens: charge moves. Electrons jump from your hair onto the balloon, leaving your hair short some electrons and the balloon with extra ones. Two objects that were neutral a moment ago now pull toward each other. That invisible tug is the same force that holds atoms together, drives lightning, and — once you can calculate it — explains everything from static cling to how a photocopier works.

This lesson makes that invisible force visible: what charge actually is, how strongly charges push and pull on each other, and how we describe the space around a charge using something called a field.

Two kinds of materials: conductors and insulators

Electric charge comes from two particles inside atoms: protons (positive) and electrons (negative). Protons sit locked in the nucleus and don't move; electrons are what actually flow from place to place. An object with more electrons than protons is negatively charged; one with fewer electrons is positively charged.

  • Conductors allow charge to move freely. In metals like copper, outer electrons are loosely held and drift through the material; in ionic solutions like salty water, it's the dissolved charged ions (not free electrons) that carry the charge from place to place. Either way, charge spreads out easily.
  • Insulators (rubber, glass, plastic, dry air) hold their electrons tightly, so charge tends to stay put wherever it was placed instead of spreading out.

That's why rubbing a balloon (an insulator) on your hair leaves the charge sitting right on the surface where you rubbed it, instead of draining away.

🔑 The core rule of charge

Like charges repel, opposite charges attract — and charge is never created or destroyed, only transferred from one object to another. Every charged object you'll ever analyze is just keeping track of where extra electrons went.

\[ F = k\dfrac{q_1 q_2}{r^2} \]
Coulomb's law: the electrostatic force between two point charges \(q_1\) and \(q_2\) separated by distance \(r\), where \(k \approx 8.99\times10^9\ \text{N}\cdot\text{m}^2/\text{C}^2\).
\[ E = \dfrac{F}{q} \]
Electric field is force per unit charge — it describes the 'push' that any charge placed at that point would feel, independent of how big that test charge happens to be.
\[ E = k\dfrac{Q}{r^2} \]
The field created by a single point charge \(Q\) at distance \(r\). Combine this with \(F = qE\) to find the force on any second charge placed nearby.
🎮 Interactive: Electric Field Around Charges LIVE
Drag charges around and watch the field lines redraw in real time. Notice how lines point away from positive charges and into negative ones, and how they bunch up close to a charge where the field is strongest.

Reading a field-line diagram

Field lines are a map, not a real physical thing — but they encode real information. Three rules let you read any diagram at a glance:

  • Lines point away from positive charges and into negative charges — that's the direction a small positive test charge would be pushed.
  • Where lines are bunched close together, the field is strong; where they spread out, it's weak. That's why the field always gets weaker as you move away from a charge.
  • Lines never cross. If they did, the field would have to point in two directions at the same point, which isn't possible.
📝 Worked example: Two small charged spheres, \(q_1 = +2\ \mu C\) and \(q_2 = +3\ \mu C\), sit 0.50 m apart. Find the force each one exerts on the other.
  1. Write Coulomb's law: \(F = k\dfrac{q_1 q_2}{r^2}\)
  2. Convert to base units: \(q_1 = 2\times10^{-6}\ \text{C}\), \(q_2 = 3\times10^{-6}\ \text{C}\), \(r = 0.50\ \text{m}\)
  3. Plug in: \(F = (8.99\times10^9)\dfrac{(2\times10^{-6})(3\times10^{-6})}{(0.50)^2}\)
  4. Numerator: \(8.99\times10^9 \times 6\times10^{-12} = 0.05394\); divide by \(0.25\): \(F \approx 0.216\ \text{N}\)
✓ F ≈ 0.216 N, pushing the spheres apart — both charges are positive, so the force is repulsive.
📝 Worked example: A point charge \(Q = +5\ \mu C\) sits alone in space. (a) What electric field does it create 0.20 m away? (b) If a second charge \(q = 3\ \mu C\) is placed at that point, what force does it feel?
  1. Field from a point charge: \(E = k\dfrac{Q}{r^2} = (8.99\times10^9)\dfrac{5\times10^{-6}}{(0.20)^2}\)
  2. Numerator: \(8.99\times10^9 \times 5\times10^{-6} = 4.495\times10^4\); divide by \(0.04\): \(E \approx 1.12\times10^6\ \text{N/C}\)
  3. Force on the second charge: \(F = qE = (3\times10^{-6})(1.12\times10^6)\)
  4. \(F \approx 3.37\ \text{N}\), pointing away from \(Q\) since both charges are positive
✓ E ≈ 1.12×10⁶ N/C at that point; the 3 μC charge placed there feels a force of about 3.37 N, pushed away from Q.
⚠️ Don't confuse the field with the force

A common mix-up: the electric field \(E\) exists at a point in space whether or not anything is there to feel it — it depends only on the source charge and the distance. The force \(F = qE\) only shows up once you place a second charge in that field, and it depends on that charge's own size and sign. Doubling the test charge doubles the force on it, but the field itself doesn't change at all. Also remember: the algebra in Coulomb's law and the field equations gives you magnitude only — whether the force is a push or a pull comes from reasoning about the signs of the charges separately (like signs repel, opposite signs attract).

Check your understanding

1. Rubbing a balloon on your hair transfers electrons from your hair to the balloon. What happens to your hair's charge?
Your hair loses electrons, so it ends up with more protons than electrons — a net positive charge. The balloon, having gained those electrons, becomes negative.
2. Which best describes why metals are good conductors of charge?
In metals, outer electrons aren't tightly bound to any one atom, so they drift freely through the material, letting charge move and redistribute easily.
3. Two charges of +4 μC and +4 μC are 1.0 m apart. If you double the distance between them to 2.0 m, what happens to the force between them?
Coulomb's law has r² in the denominator, so doubling r reduces the force by a factor of 2² = 4 — the force drops to one-quarter of its original value.
4. At a certain point near a positive charge, the electric field points to the right. If you replace the source with a negative charge of the same magnitude at the same location, what happens to the field at that point?
Field lines point away from positive charges and toward negative charges. Swapping the sign of the source charge (same magnitude) reverses the field direction but keeps its size the same.
✅ Key takeaways
  • Charge comes from electrons moving between objects; conductors let charge move freely, insulators keep it put.
  • Coulomb's law, F = kq₁q₂/r², gives the force between two charges — like signs repel, opposite signs attract, and force falls off with the square of the distance.
  • Electric field E = F/q describes the space around a charge; for a point charge, E = kQ/r². Field lines point away from positive charges and into negative ones.
  • The field exists independent of any charge placed in it; the force only appears once you put a second charge there.