Electric charge and how objects get charged
Everything is made of atoms. An atom has positive protons and negative electrons. Usually they balance, so the object is neutral.
When you rub two materials, some electrons move from one to the other. The one that gains electrons becomes negative. The one that loses electrons becomes positive.
Charge is measured in coulombs (C). One coulomb is very large, so we often use microcoulombs: 1 µC = 10⁻⁶ C. The smallest charge is the charge of one electron, e = 1.6 × 10⁻¹⁹ C. Every charge is a whole-number multiple of e. This is called quantisation of charge.
Conservation of charge
Charge is never created and never destroyed. It only moves from one object to another. So the total charge of a closed group stays the same.
Example: rub a glass rod with silk. The rod becomes +q and the silk becomes −q. Total = 0, the same as before.
When two identical metal balls touch, they share the charge equally. +6 µC and 0 → +3 µC and +3 µC. Total is still +6 µC (step 3 in the 3D).
Like charges repel, unlike charges attract
- + and + → push apart (repel)
- − and − → push apart (repel)
- + and − → pull together (attract)
The force acts along the straight line joining the two charges. Both charges feel the same size of force, in opposite directions (Newton's third law).
A charged object can also attract a neutral one, like a comb picking up small paper bits. The comb shifts the charges inside the paper a little.
Coulomb's law and point charges
A point charge is a charged object so small, compared with the distance to others, that we can treat all its charge as sitting at one point.
In 1785 Charles-Augustin de Coulomb measured the force with a twisting balance. For two point charges q₁ and q₂ at distance r:
F = k · q₁ · q₂ / r²
- k ≈ 9 × 10⁹ N·m²/C² (in air or vacuum). Also k = 1/(4πε₀), with ε₀ = 8.85 × 10⁻¹² C²/(N·m²).
- F ∝ q₁q₂: double one charge, force doubles.
- F ∝ 1/r²: double the distance, force becomes 1/4. Triple it, force becomes 1/9.
Use SI units: charge in C, distance in m, force in N. Put in sizes only; decide attract or repel from the signs.
Electric field: the idea
How does a charge push something it does not touch? Every charge makes an electric field in the space around it. Any other charge placed in that field feels a force.
Field strength E = F / q (newtons per coulomb). Near a point charge, E = kQ / r². You will learn field lines in the next lesson.
Try it: a balloon experiment
Blow up two balloons and tie threads to them. Rub both on your hair or a woollen sweater. Hang them side by side. They swing apart: same charge, repel. Now bring one near your hair: it pulls toward it. Move the balloon farther away and feel how fast the pull weakens. That fast drop is the 1/r² rule.
Key formulas and definitions
- F = k · q₁ · q₂ / r²
- k = 1/(4πε₀) ≈ 9 × 10⁹ N·m²/C²
- q = n · e, e = 1.6 × 10⁻¹⁹ C
- Total charge before = total charge after
- E = F / q
Worked examples
1. Two charges of +1 µC each are 1 m apart. Find the force.
F = 9×10⁹ × (1×10⁻⁶)(1×10⁻⁶) / 1² = 9×10⁹ × 10⁻¹² = 9×10⁻³ N = 0.009 N. Both positive, so they repel.
2. Charges +2 µC and −3 µC are 30 cm apart. Find the force and say its type.
r = 0.3 m. F = 9×10⁹ × 2×10⁻⁶ × 3×10⁻⁶ / 0.09 = 9×10⁹ × 6×10⁻¹² / 0.09 = 0.054 / 0.09 = 0.6 N. Opposite signs, so attraction.
3. The force between two charges is 8 N. The distance is doubled. What is the new force?
F ∝ 1/r². Doubling r makes r² four times bigger. New F = 8 / 4 = 2 N.
4. The force is 5 N. One charge is tripled and the distance is halved. New force?
Charge ×3 → force ×3. Distance ÷2 → force ×4. New F = 5 × 3 × 4 = 60 N.
5. Identical metal balls carry +8 µC and −2 µC. They touch and are separated. Charge on each?
Total = +8 + (−2) = +6 µC. Shared equally: +3 µC each.
6. How many electrons must be removed from a body to give it +3.2 × 10⁻¹⁹ C? And to give it +1 µC?
n = q/e. For 3.2×10⁻¹⁹ C: n = 2. For 1×10⁻⁶ C: n = 10⁻⁶ / 1.6×10⁻¹⁹ = 6.25 × 10¹² electrons.
Common mistakes
- Forgetting to change cm to m and µC to C before using F = kq₁q₂/r².
- Forgetting to square r. If r = 0.2 m, use r² = 0.04, not 0.2.
- Putting the minus sign into F. Use sizes to get F; decide attract or repel from the signs.
- Thinking the bigger charge feels a bigger force. Both charges feel the same size of force.