Conservation of Charge

Electric charge is one of the fundamental properties of matter, and like energy and momentum, it obeys a strict conservation law: the total electric charge of an isolated system never changes. This principle, known as conservation of charge, means that charge cannot be created from nothing nor destroyed — it can only be transferred from one object to another. Whether you shuffle across a carpet, rub a glass rod with silk, or witness a lightning bolt, the total charge of the universe remains exactly the same before and after. Charge comes in two varieties: positive (carried by protons) and negative (carried by electrons). The elementary charge — the magnitude of charge on a single proton or electron — is denoted e ≈ 1.602 × 10⁻¹⁹ coulombs (C). All observable charges are integer multiples of this value, a property called charge quantisation. When we say a balloon becomes negatively charged after rubbing it against hair, we mean electrons have physically transferred from the hair to the balloon; the hair loses electrons (becomes positive) and the balloon gains them (becomes negative). No net charge is created. Understanding conservation of charge lets you analyse every electrostatic charging method — friction, conduction, and induction — with confidence. In each case, you can track where every electron goes and verify that the total charge before equals the total charge after. This bookkeeping approach not only confirms the law but also forms the foundation for circuit analysis, nuclear physics, and particle physics, where charge conservation is tested to extraordinary precision.

Key takeaways
  • What Conservation of Charge Means
  • Charging by Friction
  • Charging by Conduction (Contact)
  • Charging by Induction
  • Charge Quantisation

What Conservation of Charge Means

Mathematically, for any isolated system the net charge Q_total = Q_positive + Q_negative is constant. If object A starts with charge +6e and object B with charge −2e, the system has net charge +4e. No matter how the objects interact, the combined charge must remain +4e. This is analogous to conservation of energy: you can convert forms, but the total is fixed.

Charging by Friction

When two different materials are rubbed together, electrons transfer from the surface with weaker electron affinity to the surface with stronger electron affinity. Example: rubbing glass with silk. Silk holds electrons more tightly, so electrons move from the glass to the silk. The glass loses electrons → net positive charge; the silk gains electrons → net negative charge. If the glass gains charge +Q, the silk gains charge −Q. Their sum is zero, consistent with both starting neutral. The friction does not create charge; it only provides the energy to overcome the weak binding of surface electrons.

Charging by Conduction (Contact)

A charged conductor touched to a neutral conductor shares its excess charge. If a sphere carrying charge +8 μC touches an identical neutral sphere, electrons redistribute until both are at equal potential. For identical spheres, each ends up with +4 μC. Total before: +8 μC + 0 = +8 μC. Total after: +4 μC + +4 μC = +8 μC. Charge is conserved exactly. For non-identical conductors, the split is unequal but the sum is still +8 μC.

Charging by Induction

Induction is trickier because no charge is transferred from the inducing object — yet a neutral body can be given a permanent charge. Here is the key sequence: (1) Bring a negatively charged rod near a neutral conducting sphere. (2) Electrons in the sphere are repelled to the far side; the near side becomes positive. (3) While the rod is still nearby, ground the sphere (connect to Earth). Electrons flow from sphere to ground — the sphere is now net positive. (4) Remove the ground wire, then remove the rod. The sphere retains charge +Q. Where did this charge go? The Earth absorbed charge −Q. Total charge of sphere + Earth is unchanged. Conservation is maintained at every step.

Charge Quantisation

Charge is not continuous — it exists only in discrete multiples of the elementary charge e = 1.602 × 10⁻¹⁹ C. Any measured charge Q must satisfy Q = ne, where n is an integer (positive or negative). This is why conservation of charge is absolute: electron transfer is a counting process. You can gain or lose 1, 2, 3 … electrons, but never half an electron. (Quarks have fractional charges ±e/3 and ±2e/3, but they are permanently confined inside protons and neutrons and are never observed individually.)

The Key Equation

Qtotal=Q1+Q2+⋯+Qn=constant (isolated system)Q_{\text{total}} = Q_1 + Q_2 + \cdots + Q_n = \text{constant (isolated system)}
  • Q_{\text{total}} — Total charge (coulomb (C)): The net algebraic sum of all positive and negative charges in the system.
  • Q_i — Charge of the i-th object (coulomb (C)): Individual charge, which can be positive, negative, or zero. Positive charges come from a deficit of electrons; negative charges from a surplus.
  • e — Elementary charge (coulomb (C)): The fundamental unit of charge: e = 1.602 × 10⁻¹⁹ C. All charges are integer multiples of e.

Worked Example

Problem. Three metal spheres A, B, and C are identical in size. Initially, sphere A carries charge −12 μC, sphere B carries +4 μC, and sphere C is neutral. First, A and B are touched together and then separated. Then, the combined A (after contact) is touched to C and separated. What is the final charge on each sphere?

QA=−2 μC,QB=−4 μC,QC=−2 μCQ_A = -2\,\mu C,\quad Q_B = -4\,\mu C,\quad Q_C = -2\,\mu C

Answer. Sphere A: −2 μC, Sphere B: −4 μC, Sphere C: −2 μC. Total = −8 μC (conserved).

Figure
Diagram
Charging by Induction — Charge Conservation at Each StepStep 1Neutralsphere−−−++−rodRod broughtnear sphereNet = 0Step 2++−−Ground−rodGrounded: e⁻flow to EarthSphere: +QStep 3++++−rodGround removed,rod still nearSphere: +QStep 4++++Rod removed.Sphere charged +QEarth: −Q total=0
Origins · 1 minBenjamin Franklin and how this was discovered
BF
Benjamin Franklin
1706–1790 · American

Franklin was the first to propose that electric charge is conserved. Through his experiments in the 1740s–50s he established the 'one-fluid' model of electricity, arguing that charging involved transferring a single 'electrical fluid' rather than creating it. He coined the terms positive and negative for the two states of electrification, and his key insight was that what one object gains another must lose — the earliest articulation of charge conservation. He also invented the lightning rod, a direct application of charge redistribution. Franklin's famous kite-and-key experiment in 1752 was never directly witnessed by anyone else, and Franklin himself wrote about it only after the fact — leading some historians to debate whether he actually performed it exactly as described.

  • Coulomb's Law — Coulomb's Law quantifies the force between two point charges — you need to know the values and signs of charges (established by conservation) before applying it.
  • Electric Field — The electric field is produced by charges. Understanding how charge distributes after conservation processes tells you the source of every electric field.
  • Conductors and Insulators — Whether charge can move freely (conductor) or is fixed (insulator) determines how conservation plays out during contact and induction charging.
  • Charge Conservation in Nuclear Reactions — The same law applies in nuclear and particle physics: the total charge number on both sides of any nuclear reaction equation must balance.