Aim for FivePhysics C: E&M

Unit 8 · Topic 8.2

8.2 Conservation of Electric Charge and the Process of Charging

Charge is conserved: it is never created or destroyed, only moved from one place to another. Objects become charged when electrons move onto or off them, by friction, by contact or by induction, and understanding where the electrons go lets you predict the final charges.

Key terms

  • conservation of charge
  • charging by friction
  • charging by contact (conduction)
  • charging by induction
  • polarization
  • grounding

Conservation of charge

In any process, the total charge of an isolated system stays the same. If a rod gains −4 nC by rubbing a cloth, the cloth must end up with +4 nC.

In everyday charging, it's electrons that move. Protons are locked in nuclei. So a positive object has lost electrons, and a negative object has gained them. To count them, divide the net charge by e: an object with −3.2 nC has 2.0 × 10¹⁰ extra electrons.

Three ways to charge an object

  • Friction: rubbing two different materials together transfers electrons from one to the other. They end up with equal and opposite charges.
  • Contact (conduction): touching a charged object to a neutral one lets some charge flow across. The neutral object ends up with the same sign of charge as the charged one. Two identical conducting spheres that touch end up sharing the total charge equally.
  • Induction: a charged object is brought near, but not touching, a conductor. The conductor's free electrons shift, and a ground connection lets charge flow in or out. Remove the ground first, then the charged object, and the conductor keeps a charge opposite to the nearby object.

Polarization

When a charged object comes near a neutral object, the charges inside the neutral object shift. This separation of charge, with no change in net charge, is called polarization.

In a conductor, free electrons move across the whole object: bring a negative rod near and electrons pile up on the far side, leaving the near side positive. In an insulator, each molecule just stretches a little, with its electron cloud shifting slightly to one side.

Either way, the side with the opposite charge ends up closer to the rod. Because Coulomb's law gets weaker with distance, the attraction to the near side beats the repulsion from the far side. So a charged object attracts a neutral object. That's why a charged balloon sticks to a wall and a charged comb picks up bits of paper.

Grounding

Grounding means connecting an object to the Earth with a conductor. The Earth is so large that it can give or take almost any amount of charge without its own state changing. A grounded conductor lets electrons flow in or out until it reaches the Earth's potential, which you'll learn to call zero in Unit 9.

In induction, a nearby negative rod pushes electrons from the conductor down into the ground. Cut the ground wire while the rod is still there, and the conductor is left short of electrons, so it's positive. The order matters: if you take the rod away first, the electrons simply flow back.

Worked examples

Try each one yourself first, then open the solution.

  1. Example 1Calculator allowed

    Counting electrons

    A balloon rubbed on hair ends up with a charge of −3.2 nC. How many electrons did it gain, and what charge does the hair have?

    Show the solution
    1. Step 1: Number of electrons: N=∣q∣e=3.2×10−91.60×10−19=2.0×1010N = \dfrac{\lvert q \rvert}{e} = \dfrac{3.2\times10^{-9}}{1.60\times10^{-19}} = 2.0\times10^{10}.
    2. Step 2: By conservation of charge, the hair lost those electrons, so it has +3.2 nC.

    Answer: 2.0 × 10¹⁰ electrons; the hair has +3.2 nC

  2. Example 2Calculator allowed

    Identical spheres touching in turn

    Identical small conducting spheres A, B and C start with charges +8.0 nC, −2.0 nC and 0. A touches B and they are separated. Then A touches C and they are separated. Find the final charge on each sphere.

    Show the solution
    1. Step 1: A and B share their total charge equally, since they are identical: (8.0 + (−2.0)) ÷ 2 = +3.0 nC each.
    2. Step 2: Now A (+3.0 nC) touches C (0): (3.0 + 0) ÷ 2 = +1.5 nC each.
    3. Step 3: Check conservation: 1.5 + 3.0 + 1.5 = 6.0 nC, the same as the starting total 8.0 − 2.0 + 0 = 6.0 nC.

    Answer: A: +1.5 nC, B: +3.0 nC, C: +1.5 nC

  3. Example 3Calculator allowed

    Charging by induction, step by step (classic trap)

    A negatively charged rod is held near (not touching) a neutral metal sphere on an insulating stand. The sphere is touched with a grounded wire, the wire is removed, and then the rod is taken away. What is the final charge on the sphere? What if the rod had been removed before the wire?

    Show the solution
    1. Step 1: The rod repels the sphere's free electrons, so they shift to the far side. The near side is left positive.
    2. Step 2: With the ground wire connected, the repelled electrons flow out of the sphere into the ground.
    3. Step 3: Removing the wire traps the sphere with too few electrons. Removing the rod afterward lets the remaining charge spread evenly over the surface. The sphere is positive.
    4. Step 4: If the rod were removed while the ground was still connected, electrons would flow back from the ground and the sphere would end up neutral.

    Answer: Positive, opposite to the rod. Removing the rod first leaves it neutral.

Common mistakes

  • Saying protons moved to make an object positive. In these processes electrons move; a positive object has lost electrons.
  • Thinking a neutral object can't be attracted by a charged one. Polarization puts opposite charge closer, so it is attracted.
  • Giving the induced charge the same sign as the rod. Charging by induction leaves the opposite sign; charging by contact leaves the same sign.
  • Splitting charge equally between conductors of different sizes. Equal sharing only works for identical conductors (see 10.2).

On the exam

  • Questions often ask you to explain each step of an induction process. Name where electrons move and why, and say which connection is broken first.
  • When a question gives several touches in a row, track the charge after each one and check that the total never changes.

Connected topics

Videos

Check yourself

4 questions on 8.2 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

Three identical small conducting spheres start with charges A = +6.0 nC, B = 0 and C = −2.0 nC. A touches B and they are separated. Then B touches C and they are separated. What is the final charge on C?

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 there, the sphere is briefly connected to ground and then disconnected. Finally the rod is taken away. What is the sphere's final charge?

Question 3 of 4Calculator allowed

A balloon rubbed on a sweater ends up with a charge of −3.2 nC. The sweater was neutral before. How many electrons moved, and what is the sweater's charge now?

Question 4 of 4Calculator allowed

A positively charged rod picks up small bits of neutral paper. Which explanation is correct?

0 of 4 answered