Exercises: Conservation of Charge: Induction, Conduction and Polarization

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.

Classify each situation as charging by conduction, charging by induction, or polarization:

1. a) A charged rod touches a neutral metal sphere, and the sphere becomes charged.
2. b) A charged rod is brought near, but does not touch, a neutral insulating piece of paper, and the paper's charges shift slightly.
3. c) A charged rod is brought near a neutral metal sphere, the sphere is briefly grounded, and then the ground and rod are removed.

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?

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.

1. a) State the sign of the charge on A and on B.
2. b) Explain how the process shows conservation of charge.
3. c) Identify which kind of charge actually moved.

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.

1. a) Find the net charge on the balloon, including its sign.
2. b) Find the net charge on her hair, assuming only the balloon and her hair exchanged charge.
3. c) Explain why the balloon sticks to the wall even though the wall is neutral.

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.

1. a) Find the charge on each sphere afterward.
2. b) Show that the total charge is conserved.
3. 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 to C, separates them, and finally touches C to A.

1. a) Find the charge on each sphere after every step, in terms of $Q$.
2. b) Verify that the total charge is the same after every step.
3. 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.

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.

1. a) Explain why Aaliyah's hair strands spread apart, describing the charge on each strand and the forces involved.
2. b) For the electroscope, describe where the charges move in the knob, stem, and leaves, and give the net charge of the whole electroscope.
3. 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.