Conservation of Charge: Induction, Conduction and Polarization
You walk across a carpet in socks, reach for a metal doorknob, and zap! Nothing was added to your body out of thin air. Something already in the materials moved. What moved, and where did it end up? By the end of this page you will be able to answer that, and also explain why a charged balloon sticks to a perfectly neutral wall.
Charge comes from moving electrons
Every atom has positive protons and neutral neutrons in its nucleus, and negative electrons around it. A neutral object has equal amounts of positive and negative charge, so the total is zero.
An object becomes charged when it has an unequal number of protons and electrons. Protons are locked inside nuclei, so in everyday situations only electrons move.
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Gain electrons: the object becomes negative.
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Lose electrons: the object becomes positive.
Charge is measured in coulombs (C). One electron has a charge of magnitude $e = 1.60 \times 10^{-19}\ \text{C}$, so any charge is a whole number of these:
$$q = N e$$where $N$ is the number of extra (or missing) electrons.
So if a rod gains $3.0 \times 10^{-9}\ \text{C}$ of negative charge, the fur loses exactly that many electrons and ends up with $+3.0 \times 10^{-9}\ \text{C}$. The total stays zero.
Sofia rubs a plastic rod with a piece of fur, and the rod becomes negatively charged. Explain what kind of charged particle moved between the fur and the rod, and state…
Sofia rubs a plastic rod with a piece of fur, and the rod becomes negatively charged. Explain what kind of charged particle moved between the fur and the rod, and state whether the fur becomes positively charged, negatively charged, or stays neutral.
Olivia rubs a balloon on her hair. The balloon then sticks to a neutral wall. The balloon gained $5.0 \times 10^{10}$ electrons, each of charge…
Olivia rubs a balloon on her hair. The balloon then sticks to a neutral wall. The balloon gained $5.0 \times 10^{10}$ electrons, each of charge $1.60 \times 10^{-19}\ \text{C}$ in magnitude.
- a) Find the net charge on the balloon, including its sign.
- b) Find the net charge on her hair, assuming only the balloon and her hair exchanged charge.
- c) Explain why the balloon sticks to the wall even though the wall is neutral.
Conductors and insulators
In a conductor (metals, salt water, your body), some electrons are free to move through the whole material. In an insulator (plastic, glass, rubber, dry paper), electrons stay bound to their own atoms and cannot travel far.
This is why charge you put on plastic stays where you put it, while charge on a metal sphere spreads out across the whole surface.
| Conductor | Insulator | |
|---|---|---|
| Electrons | free to move | bound to atoms |
| Examples | copper, aluminum, steel | plastic, glass, rubber |
| Added charge | spreads over the surface | stays in place |
A neutral electroscope has its metal leaves hanging together. Jayden touches the metal knob with a negatively charged rod. What happens to the leaves, and why?
A neutral electroscope has its metal leaves hanging together. Jayden touches the metal knob with a negatively charged rod. What happens to the leaves, and why?
Charging by conduction
Conduction means charging by direct contact. A charged object touches a neutral conductor, and charge flows between them until both are at the same state.
A leaf electroscope shows this well: a metal knob, a stem, and two thin metal leaves hanging together. Touch the knob with a negative rod. Electrons flow from the rod onto the electroscope and spread over the knob, stem, and leaves. Both leaves now carry negative charge, repel each other, and spread apart. The more charge, the wider the spread.
When a charged conductor touches a neutral conductor, the neutral object ends up with the same sign as the charged object that touched it.
When two identical conducting spheres touch, they share the total charge equally.
Two identical metal spheres carry charges of $+6.0\ \mu\text{C}$ and $-2.0\ \mu\text{C}$. They are touched together and then separated. a) Find the charge on each sphere…
Two identical metal spheres carry charges of $+6.0\ \mu\text{C}$ and $-2.0\ \mu\text{C}$. They are touched together and then separated.
- a) Find the charge on each sphere afterward.
- b) Show that the total charge is conserved.
- c) Predict whether the spheres attract or repel each other afterward.
You have three identical, insulated metal spheres, A, B, and C. Sphere A has charge $+Q$, and B and C are neutral. Ethan touches A to B, separates them, then touches B…
You have three identical, insulated metal spheres, A, B, and C. Sphere A has charge $+Q$, and B and C are neutral. Ethan touches A to B, separates them, then touches B to C, separates them, and finally touches C to A.
- a) Find the charge on each sphere after every step, in terms of $Q$.
- b) Verify that the total charge is the same after every step.
- c) Find the final ratio of the force between A and C to the force that would act between A and C if they started with $+Q$ and $0$ at the same separation. Assume the same separation each time.
Charging by induction
Induction charges an object without touching it. The result is a charge of the opposite sign to the rod. Here are the steps for a metal sphere on an insulating stand:
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Bring a negative rod near the neutral sphere (no contact). Free electrons in the sphere are repelled to the far side, so the near side is positive and the far side is negative.
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Ground the sphere by touching it with a finger or a wire to the ground. Electrons flow off the sphere to the ground, away from the rod.
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Remove the ground connection first, with the rod still nearby. The extra electrons cannot come back.
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Remove the rod. The sphere is left with a net positive charge, spread over its surface.
Where did the electrons that left go? Into the ground. The sphere plus the ground is still neutral overall, so charge is conserved.
Another way to induce charge: touch two neutral metal spheres together, bring a rod near one, separate the spheres while the rod is still there, then remove the rod. The spheres end up with equal and opposite charges. A positive rod pulls electrons toward the near sphere A, so A becomes negative and B, which lost electrons, becomes positive.
Classify each situation as charging by conduction, charging by induction, or polarization: a) A charged rod touches a neutral metal sphere, and the sphere becomes…
Classify each situation as charging by conduction, charging by induction, or polarization:
- a) A charged rod touches a neutral metal sphere, and the sphere becomes charged.
- b) A charged rod is brought near, but does not touch, a neutral insulating piece of paper, and the paper's charges shift slightly.
- c) A charged rod is brought near a neutral metal sphere, the sphere is briefly grounded, and then the ground and rod are removed.
Two identical neutral metal spheres, A and B, touch each other. A positively charged glass rod is brought near A, without touching, and then the spheres are separated…
Two identical neutral metal spheres, A and B, touch each other. A positively charged glass rod is brought near A, without touching, and then the spheres are separated while the rod is still nearby. Finally the rod is removed.
- a) State the sign of the charge on A and on B.
- b) Explain how the process shows conservation of charge.
- c) Identify which kind of charge actually moved.
Polarization
An insulator cannot move electrons across the whole object, but inside each atom or molecule the electrons can shift slightly. When a charged rod comes near, the charges in the insulator separate a little: the side near the rod gets the opposite charge, the far side gets the same charge. This is polarization. The object as a whole is still neutral.
Because the opposite charge is closer to the rod, the attraction is slightly stronger than the repulsion. The net force is attractive.
This explains why a rubbed balloon sticks to a wall, why bits of paper jump to a comb, and why a charged rod can pick up neutral foam pieces. Notice that neutral objects can be attracted, but they are never repelled by a charged object.
At a science museum, Aaliyah touches a Van de Graaff generator, and her hair stands up. Later, a student brings a negatively charged rod near a neutral electroscope…
At a science museum, Aaliyah touches a Van de Graaff generator, and her hair stands up. Later, a student brings a negatively charged rod near a neutral electroscope without touching it, and the leaves spread apart.
- a) Explain why Aaliyah's hair strands spread apart, describing the charge on each strand and the forces involved.
- b) For the electroscope, describe where the charges move in the knob, stem, and leaves, and give the net charge of the whole electroscope.
- c) Explain how you could use grounding to leave the electroscope with a permanent positive charge, and describe what the leaves do at each step.
Summary
Back to the zap from the doorknob: electrons moved from the carpet to your socks and body, and when your finger neared the metal, they jumped across the gap. Charge was transferred, never created.