Aim for FivePhysics 2

Unit 10 · Topic 10.2

10.2 Conservation of Electric Charge and the Process of Charging

Charge is conserved: an object's net charge changes only when charge, usually electrons, moves onto or off it. Rubbing, touching, polarization, grounding and induction are the ways objects get charged or rearrange their charge. This topic explains static cling, balloons on walls and why lightning rods are grounded.

Key terms

  • conservation of charge
  • charging by friction
  • charging by conduction
  • charging by induction
  • polarization
  • grounding

Conservation of charge

Charge can't be created or destroyed, only moved. If a system's net charge changes, exactly that much charge crossed its boundary. In ordinary charging, it's electrons that move; protons are locked inside nuclei. An object becomes negative by gaining electrons and positive by losing them.

The number of electrons transferred is the charge divided by e. A charge of just 1 nC means about 6 billion extra or missing electrons.

Charging by friction and by contact

Friction (rubbing): when two different materials rub together, electrons move from one to the other. Rub a balloon on your hair and electrons move onto the balloon, leaving the balloon negative and your hair positive by the same amount.

Contact (conduction): when a charged conductor touches a neutral or differently charged conductor, charge flows until both surfaces are at the same electric potential. Two identical conducting spheres that touch end up sharing the total charge equally.

Polarization

A charged object can rearrange the charges in a nearby neutral object without touching it. Bring a negative rod near a neutral metal can, and the can's free electrons are pushed to the far side, leaving the near side positive. The can is still neutral overall, but it's polarized.

In an insulator, electrons can't travel across the object, but each atom or molecule shifts slightly, so the near surface still ends up with a slight opposite charge.

Polarization is why a charged object attracts a neutral one. The opposite charges on the near side are closer than the like charges on the far side, and since electric force weakens with distance, the attraction wins. That's how a rubbed balloon sticks to a neutral wall.

Grounding and charging by induction

Grounding connects an object to a huge, nearly neutral reservoir of charge, usually Earth. Charge flows between the object and the ground as needed, so the object ends up neutral unless a nearby charge pushes or pulls charge on or off it.

Charging by induction gives an object a charge without touching it with the charged object:

  • Bring a negatively charged rod near a neutral metal sphere. The sphere polarizes: electrons are pushed to the far side.
  • Ground the sphere, for example by touching it. Electrons, pushed by the rod, flow from the sphere into the ground.
  • Remove the ground connection while the rod is still nearby. The electrons can't come back.
  • Remove the rod. The sphere is left positive, the opposite sign to the rod, and the extra charge spreads over its surface.

Worked examples

Try each one yourself first, then open the solution.

  1. Example 1Calculator allowed

    Touching identical spheres

    Identical metal spheres A (+6.0 nC) and B (−2.0 nC) are touched together and then separated. What is the charge on each, and how many electrons moved, and in which direction?

    Show the solution
    1. Step 1: Total charge is conserved: +6.0 + (−2.0) = +4.0 nC.
    2. Step 2: Identical conductors share it equally: +2.0 nC each.
    3. Step 3: B went from −2.0 nC to +2.0 nC, a change of +4.0 nC, so B lost electrons to A. Number moved = (4.0 × 10⁻⁹ C)/(1.60 × 10⁻¹⁹ C) = 2.5 × 10¹⁰ electrons.

    Answer: Each sphere ends at +2.0 nC; 2.5 × 10¹⁰ electrons moved from B to A

  2. Example 2

    Charging by induction (classic trap)

    A positively charged rod is held near a neutral metal sphere on an insulating stand. The sphere is briefly grounded on the side away from the rod, then the ground is removed, then the rod is taken away. What is the sign of the sphere's final charge? A student says “positive, because the rod is positive.” Explain why that's wrong.

    Show the solution
    1. Step 1: The positive rod attracts electrons toward the near side of the sphere.
    2. Step 2: When the sphere is grounded, more electrons are pulled up from the ground into the sphere, because the rod attracts them.
    3. Step 3: With the ground removed first, those extra electrons are trapped. When the rod leaves, the sphere has more electrons than protons.
    4. Step 4: Induction always gives the opposite sign to the inducing charge. The student was thinking of charging by contact.

    Answer: Negative

Common mistakes

  • Saying protons move during charging. In solids, electrons move; a positive object has lost electrons.
  • Thinking a neutral object can't be attracted to a charged one. Polarization makes the near side opposite in sign, so there's a net attraction.
  • Removing the rod before the ground in induction. Then the charge flows back and the object ends up neutral.
  • Assuming touching always splits charge equally. That's only true for identical conductors.

On the exam

  • Expect to draw charge distributions on objects at each step of a charging process, and to justify the final sign.
  • Questions often ask you to explain an attraction between a charged and a neutral object using polarization and the distance dependence of Coulomb's law.

Connected topics

Videos

Check yourself

4 questions on 10.2 Conservation of Electric Charge and the Process of Charging. Pick an answer to see if you got it, and why.

Question 1 of 4Calculator allowed

A plastic rod is rubbed with wool and ends up with a charge of −8.0 nC. How many electrons moved, and in which direction?

Question 2 of 4Calculator allowed

A negatively charged rod is held near, but not touching, a neutral metal sphere on an insulating stand. While the rod is still nearby, the sphere is briefly connected to the ground with a wire, and then the wire is removed. Finally the rod is taken away. What is the final charge on the sphere?

Question 3 of 4Calculator allowed

Two identical metal spheres carry charges of +6.0 nC and −2.0 nC. They are touched together and then separated. What is the charge on each sphere afterward?

Question 4 of 4Calculator allowed

Three identical metal spheres start with charges A = +8q, B = 0 and C = −4q. Sphere A touches B, and they are separated. Then B touches C, and they are separated. What is the final charge on C?

0 of 4 answered