8.2 Electric Charge and the Process of Charging

TLDR

Electric charge is conserved: it can move between objects but is never created or destroyed. In AP Physics C: E&M, you need to explain three ways to change an object's charge state (friction, contact, and induction), describe polarization in neutral objects, and use grounding to reason about how charge flows to or from Earth.

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Why This Matters for the AP Physics C: E&M Exam

This topic sits inside Unit 8, which carries one of the larger shares of the multiple-choice section. Charging questions reward clear, model-based reasoning rather than heavy calculation, so they show up well in both quick conceptual multiple-choice items and in written explanations.

The first free-response question on the exam focuses on creating and using mathematical models and representations, and it can pull from any unit. Charging and conservation of charge give you practice with the skills that question rewards: drawing charge diagrams, applying a definition or principle to make a claim, and justifying that claim with evidence. Expect to:

• Diagram how charge shifts during friction, contact, and induction.
• Compare charge states before and after a process using conservation of charge.
• Explain why a neutral object can still feel an attractive force.

Key Takeaways

• Charge is conserved. The total charge of an isolated system stays constant; charging only redistributes existing charge.
• Charging usually means electron transfer. Electrons move because they are the mobile charge carriers; protons stay put.
• Friction and contact transfer net charge between objects. Induction does not require contact.
• Polarization is induced charge separation with no change in net charge. It can happen in neutral objects, which is why a charged object can attract neutral bits of paper.
• Grounding connects an object to a much larger, roughly neutral system (like Earth) that can supply or absorb electrons.
• In charging by induction, grounding while the charged object is nearby lets you leave the object with a net charge opposite to the inducing charge.

Conservation of Charge

A system's net charge or internal charge distribution can change because of the presence of another charged system, or because that other system's charge distribution changes. This explains charging by friction, charging by contact, and induced charge separation (polarization). The distribution of charge can shift, but the total charge stays constant. That conservation rule is the backbone of every charging process.

A system can also respond when a nearby system's charge distribution changes over time. If charges in a nearby conductor rearrange, the electric forces on your system change and can cause its own charge distribution to readjust.

Charge Distribution Changes

• Friction or contact between systems changes the net charge of a system.
  • Rub a balloon on hair and electrons transfer from the hair to the balloon.
  • The balloon gains negative charge while the hair loses electrons and becomes positively charged.
  • Total charge is conserved, just redistributed between the two objects.
• Polarization happens when the electrostatic force between two systems redistributes charge within them.
  • This is induced charge separation with no transfer of net charge.
  • When a charged rod approaches a neutral metal sphere, electrons in the sphere shift.
  • The side facing the rod develops charge opposite to the rod.
  • The far side develops the same type of charge as the rod.
• Neutral systems can experience induced charge separation without gaining or losing net charge.
  • A charged balloon can attract neutral paper bits through polarization.
  • The balloon induces opposite charge on the near side of the paper.
  • The attractive force on the near (opposite) charges beats the repulsive force on the far (like) charges because those near charges are closer.
  • The result is a net attractive force pulling the paper toward the balloon.

Charge Transfer Between Systems

The net charge of a system changes only through transfer of charge between the system and its surroundings. This follows conservation of charge strictly.

Electrons are usually the charge carriers that move during charging because they are less tightly bound to atoms than protons.

• When charging occurs, electrons move from one system to another.
  • Gain electrons, become negatively charged.
  • Lose electrons, become positively charged.
  • Total charge before and after the transfer stays the same.
• Without any transfer to or from a system, its net charge stays constant.
  • An isolated charged object holds its charge indefinitely under ideal conditions.
  • In reality, charged objects slowly lose charge to surrounding air molecules.

Grounding Charged Objects

Grounding means electrically connecting a charged object to a much larger, approximately neutral system, usually Earth. This lets charge flow between the object and the ground.

Earth acts as a huge reservoir of charge that can supply or accept electrons as needed:

• Grounding a positively charged object:
  • Electrons flow from Earth into the object.
  • The object neutralizes as it regains the electrons it had lost.
• Grounding a negatively charged object:
  • Excess electrons flow from the object into Earth.
  • The object neutralizes as it loses its extra electrons.
• Grounding is key to charging by induction:
  • A charged rod brought near a metal object causes charge separation.
  • If the metal is grounded while the rod is nearby, charge flows to or from ground.
  • Remove the ground connection (rod still nearby), and the object keeps a net charge.
  • This charges the object without direct contact with the rod.

How to Use This on the AP Physics C: E&M Exam

Problem Solving

Treat charge like a quantity that has to balance. Write the total charge before a process and set it equal to the total after. If two objects start neutral and one ends up at $+8.0 \times 10^{-9}$ C, the other must be $-8.0 \times 10^{-9}$ C.

When a problem walks through induction step by step, track the rod, the ground, and the object separately at each stage. The order matters: ground while the rod is present, then remove the ground, then remove the rod.

Free Response

For explanation prompts, lead with the principle (conservation of charge or polarization), then apply it to the specific setup, then justify your claim with the charge motion you described. A clear charge diagram showing where electrons move often earns points and keeps your reasoning organized.

Common Trap

Induction leaves an object with charge opposite to the inducing rod, while contact leaves it with charge of the same sign as the source. Mixing these up is one of the most common mistakes on charging questions.

Practice Problem 1: Charging by Friction

Solution

By conservation of charge, the total charge before and after must match. Before rubbing, both the glass rod and silk cloth were neutral (net charge zero).

After rubbing:

• The glass rod has a charge of +8.0 × 10^-9 C.
• Conservation requires (+8.0 × 10^-9 C) + (charge on silk) = 0.
• So the charge on the silk is -8.0 × 10^-9 C.

The process was electron transfer. The glass rod lost electrons to the silk cloth during rubbing. Since electrons carry negative charge, the glass rod became positively charged (electron deficient) and the silk became negatively charged (electron rich).

Practice Problem 2: Charging by Induction

Solution

This is charging by induction, which goes in order:

1. The metal sphere starts neutral, with equal positive and negative charge.

2. The positive rod attracts mobile electrons toward it. Charge redistributes within the sphere (polarization): the near side becomes negative, the far side is left positive from an electron deficit.

3. Grounding the sphere while the rod is present lets electrons flow from ground into the sphere, pulled by the positive charge on the far side. This neutralizes that positive charge.

4. Removing the ground connection while the rod is still present leaves the sphere with excess negative charge.

5. Removing the rod lets the excess negative charge spread evenly over the sphere.

The final sphere is negatively charged, with no direct contact between the rod and sphere. That is the signature of charging by induction.

Practice Problem 3: Polarization

Solution

This is polarization of neutral objects near a charged object:

1. The neutral paper has equal positive and negative charge spread evenly throughout.

2. The negative ruler repels electrons in the paper, pushing them away from the ruler.

3. This creates a charge separation in the paper:

   • The side closer to the ruler becomes partially positive.
   • The side farther away becomes partially negative.

4. The positive charges on the paper sit closer to the ruler than the negative charges on the paper do.

5. By Coulomb's law, force varies inversely with the square of distance, so the attraction between the near positive charges and the negative ruler is stronger than the repulsion between the far negative charges and the ruler.

6. The result is a net attractive force, pulling the paper toward the ruler even though its net charge is zero.

This is why neutral objects can be attracted to charged objects through polarization.

Common Misconceptions

• "Charging creates charge." Charging never creates or harms charge. It only moves existing charge from one place to another.
• "Protons move during charging." In almost all charging situations the electrons move; protons stay locked in the nuclei.
• "Induction and contact give the same result." Contact (and friction) leaves an object charged with the same sign as the source. Induction with grounding leaves it with the opposite sign.
• "Polarization means the object gained net charge." Polarization only separates existing charge within a neutral object. The net charge is still zero.
• "A neutral object can't be attracted to a charged object." It can, through polarization, because the closer induced charges feel a stronger force than the farther ones.
• "Grounding always means adding electrons." Grounding lets electrons flow either direction. A positive object gains electrons from Earth; a negative object sends electrons to Earth.

Related AP Physics C: E&M Guides

• 8.1 Electric Charge and Electric Force
• 8.3 Electric Fields
• 8.4 Electric Fields of Charge Distributions
• 8.6 Gauss's Law
• 8.5 Electric Flux