Electric charge and conservation
What charge is, how much one coulomb represents, and why circuit currents do not require charge to disappear.
- Define electric charge and its SI unit.
- Use the elementary charge to connect microscopic carriers to macroscopic charge.
- Apply charge conservation to simple accumulation/flow arguments.
- Distinguish net charge from the existence of mobile charge carriers.
A copper wire contains an enormous number of electrons. Yet an ordinary uncharged wire is described as electrically neutral. How can both statements be true?
The key is to separate three ideas that beginners often merge: charged particles can be present, a body can have a net charge, and charge can move. They are related, but they are not the same statement.
01.1Charge is a physical quantity
We denote macroscopic electric charge by Q and measure it in coulombs. The elementary charge has the exact SI magnitude
An electron carries −e and a proton +e. If an isolated object has net charge Q, the magnitude of the corresponding elementary-charge imbalance is
Example 1. For Q=+1.00 nC,
The plus sign tells us the object has a positive net imbalance. The number is huge on a human scale, yet it can still be a minute imbalance relative to all the positive and negative charge already present in the material.
01.2Quantized microscopically, effectively continuous in ordinary circuits
At microscopic scale, ordinary transferred charge comes in integer multiples of e. At circuit scale, however, even 1 pC corresponds to more than six million elementary charges. Treating Q as a continuous variable is therefore normally an excellent approximation.
01.3Neutrality does not mean “no charge carriers”
A neutral metal contains positive ionic charge and negative electronic charge whose totals nearly cancel. Some electrons are mobile, so the metal can conduct even though its net charge is close to zero.
This distinction prevents a common misconception: current is not evidence that a wire must carry a large net negative charge.
01.4Conservation of charge: nothing can disappear from the bookkeeping
Imagine a boundary around any region. During a finite interval, stored charge changes only if a net amount of charge crosses that boundary:
Example 2. If 8 µC enters and 5 µC leaves,
The positive result means the region contains 3 µC more net positive charge than before, relative to our sign convention.
Later, once current has been defined as charge flow per unit time, this same physical principle becomes the reason branch currents must balance at a circuit node.
01.5Reasoning example: excess electrons are an imbalance, not the whole electron population
A small metal object acquires Q=−4.0 nC. The magnitude of the excess-electron count is
This counts only the excess relative to neutrality. It does not tell us the total number of electrons already present in the object.
Sanity check — what changes for +4.0 nC?
01.6Practice for mastery
- Explain how a conductor can be neutral and still conduct current.
- How many elementary charges correspond to 250 pC in magnitude?
- A region receives 12 µC and releases 15 µC. Find ΔQstored.
- Why is continuous-Q modelling normally safe in ordinary circuit analysis?
Solutions
1. Mobile carriers may exist while total positive and negative charge nearly cancel.
2. N≈1.56×109.
3. ΔQstored=−3 µC.
4. Circuit-scale charges contain enormous numbers of elementary charges, so discreteness is negligible in the usual operating regime.
Charge tells us what is conserved. The next chapter introduces voltage, which tells us how electrical energy changes per unit charge between two references.