AcademyElectric Charge and Fields
Academy
Electric Charge
Level 1 - Physics topic page in Electric Charge and Fields.
Principle
Electric charge is a conserved scalar property that appears in positive and negative units of the elementary charge.
Notation
\(q,Q\)
electric charge
\(\mathrm{C}\)
\(e\)
elementary charge magnitude
\(\mathrm{C}\)
\(N\)
integer number of elementary charges
1
\(n_p,n_e\)
numbers of protons and electrons
1
\(Q_{\mathrm{tot}}\)
total charge of an isolated system
\(\mathrm{C}\)
Method
Derivation 1: Build net charge from carriers
Ordinary matter contains positive proton charge and negative electron charge. Net charge is the algebraic sum of those contributions.
Proton contribution
\[Q_p=n_p e\]
Electron contribution
\[Q_e=-n_e e\]
Net charge
\[Q=(n_p-n_e)e\]
Derivation 2: Quantization and conservation
Charge changes by moving charged particles, not by creating arbitrary fractions of charge in macroscopic matter.
Quantized charge
\[q=Ne\qquad N\in\mathbb{Z}\]
Isolated system
\[\Delta Q_{\mathrm{tot}}=0\]
Charges may move inside the system, but the algebraic total is unchanged.
Transfer between bodies
\[\Delta Q_A=-\Delta Q_B\]
Rules
These are the compact results from the charge model above.
Elementary charge
\[e=1.60\times10^{-19}\,\mathrm{C}\]
Quantized charge
\[q=Ne\]
Net matter charge
\[Q=(n_p-n_e)e\]
Charge conservation
\[\Delta Q_{\mathrm{tot}}=0\]
Examples
Question
A small object gains
\[2.5\times10^8\]
electrons. Find its change in charge.Answer
Gaining electrons gives negative charge.
\[\Delta Q=-(2.5\times10^8)(1.60\times10^{-19})=-4.0\times10^{-11}\,\mathrm{C}\]
Checks
- Positive and negative charges add algebraically.
- A neutral object has zero net charge, not zero charged particles.
- Charge transfer changes where charge is, not the isolated total.
- A physical charge must be an integer multiple of \(e\).