Electric Charges · 10.1
Charge, Conservation & Quantisation
Electric charge comes in positive and negative forms. Ordinary charging moves electrons; it does not manufacture charge or move protons between solid objects.
Build the model
Follow charge, then explain the effect.
An object is neutral when its total positive and negative charges balance—not when it contains no charge. Losing electrons leaves a positive net charge; gaining electrons leaves a negative net charge. In an isolated system, every transferred electron changes two objects by equal and opposite amounts.
- Simple definition
- Electric charge is a conserved property of matter that can be positive or negative and occurs in whole-number multiples of the elementary charge.
- Example
- When a balloon gains electrons from hair, the balloon becomes negative and the hair becomes equally positive overall.
Charge comes in fixed packets: any charge is a whole number of elementary charges e — never a fraction.
n is an integer and e = 1.602 × 10⁻¹⁹ C is a positive magnitude
Each electron carries exactly one negative packet of charge.
An electron contributes one negative elementary charge
Charge is never created or destroyed, only moved — the totals before and after any process match.
For an isolated system, net charge stays constant
Name the imbalance
Count missing or excess electrons relative to the neutral state. Missing electrons give +ne; excess electrons give −ne.
Keep a charge ledger
If n electrons leave object A and arrive at object B, ΔQA = +ne and ΔQB = −ne, so the combined change is zero.
Use a modern atom model
Electrons occupy quantum states described by probability clouds. They are not tiny planets following fixed circular paths around a nucleus.
Change one variable at a time
Make the invisible charge model visible.
Positive slider values mean electrons leave A and arrive at B. Reverse the slider to reverse the transfer.
Charge on A+6.408e-19 C
Charge on B−6.408e-19 C
System total0 C
Smallest stepe = 1.602 × 10⁻¹⁹ C
Catch the common trap
Predict the sign and direction first.
A neutral object gains 5 electrons. What is its final charge?
Choose an answer to test the model.
Worked examples
State the model, calculate, then test the result.
EasyHow many elementary charges make up −4.8 × 10⁻¹⁹ C?
- n = Q/e = 4.8 × 10⁻¹⁹ ÷ 1.6 × 10⁻¹⁹.
- n = 3 — three excess electrons.
Answer3 electrons
MediumA small sphere loses 2.5 × 10¹³ electrons. Find its final charge if it was initially neutral.
- Losing electrons leaves a positive charge, so decide the sign before multiplying.
- Q = ne = (2.5 × 10¹³)(1.602 × 10⁻¹⁹ C).
- Round to the precision of the electron count and keep the positive sign.
AnswerQ = +4.0 × 10⁻⁶ C = +4.0 μC
HardA charged rod transfers 5.0 × 10¹⁰ electrons to a neutral sphere each second for 4.0 s. Find the sphere's final charge and the average transfer current.
- Total electrons = 2.0 × 10¹¹; Q = ne = 2.0 × 10¹¹ × 1.6 × 10⁻¹⁹ = 3.2 × 10⁻⁸ C (negative).
- I = Q/t = 3.2 × 10⁻⁸ ÷ 4.0.
- I = 8.0 nA.
AnswerQ = −32 nC; I = 8.0 nA
ChallengingCould an isolated droplet carry a charge of 2.4 × 10⁻¹⁹ C? Use quantisation to decide, and describe Millikan's logic.
- Q/e = 2.4 ÷ 1.6 = 1.5 — not a whole number.
- Charge only comes in integer multiples of e, so this value is impossible for a real droplet.
- Millikan measured many droplet charges and found every one a multiple of the same basic step — that step is e.
AnswerNo — 1.5e is forbidden; charge is quantised in whole e steps