#AP Physics 2: Electrostatics - Charging & Conservation of Charge ⚡

Hey there, future AP Physics 2 champ! Let's break down electrostatics and get you feeling confident for the exam. We'll cover charging, conservation of charge, and how it all ties together. Remember, you've got this!

#Charging Objects: The Basics

At its core, charging is all about moving electrons around. It's not about creating charge, but rather redistributing it. Think of it like shuffling a deck of cards—the total number of cards stays the same, but their arrangement changes. This process can happen in a few ways:

• Friction: Rubbing two materials together can transfer electrons from one to the other. For example, rubbing a balloon on your hair makes the balloon negatively charged (it gains electrons) and your hair positively charged (it loses electrons).
• Contact: Touching a charged object to a neutral one can transfer charge. Imagine touching a doorknob after shuffling across the carpet; the shock you feel is the transfer of electrons.
• Induced Charge Separation: Bringing a charged object near a neutral one can cause the charges within the neutral object to shift, creating a polarized object. This happens without direct contact. Think of it like a magnet attracting iron filings—the filings don’t gain or lose magnetism, but they rearrange themselves.

#Why is Understanding Charging Important?

Understanding charging is key to grasping electrostatic interactions. It explains:

• Attraction and Repulsion: Like charges repel, and opposite charges attract. This is the foundation of electric forces.
• Grounding: Connecting a charged object to the Earth allows excess charge to flow away, neutralizing the object.
• Electrical Applications: Charging is the basis for many technologies, from capacitors in electronics to electrostatic painting.

#Conservation of Charge

#How Systems Behave

Conservation of charge is a fundamental principle. It states that the total charge in an isolated system remains constant. This means that charge is neither created nor destroyed, only transferred from one object to another.

Changes in a system’s net charge or charge distribution happen due to:

• Presence of other charged systems: Nearby charged objects can influence the charge distribution within a system.
• Changes in other systems: If a nearby system's charge changes, it can affect the charge of the system you're analyzing.

Net charge of a system changes because of:

• Friction: Rubbing materials together transfers electrons.
• Contact: Touching a charged object to another allows charge to flow.
• Induced Charge Separation: When an electrostatic force between two systems redistributes charges within the systems, even neutral systems can become polarized.

#Grounding

Grounding is like giving excess charge a highway to Earth. When a charged object is connected to the Earth, which is a massive, neutral system, excess charge flows to or from the Earth until the object becomes neutral. Think of it like a giant sponge that can absorb or donate electrons without changing its own charge significantly. 🌍

#Boundary Statements

Don't worry about complex, asymmetrical charge distributions—the exam will focus on scenarios with clear patterns and symmetries.

#Practice Questions

Practice Question

Multiple Choice Questions:

1. A neutral metal sphere is touched by a negatively charged rod. Which of the following correctly describes the charge on the sphere and the charge on the rod after they are separated? (A) Sphere: negative, Rod: negative (B) Sphere: positive, Rod: negative (C) Sphere: negative, Rod: neutral (D) Sphere: neutral, Rod: negative

2. Two initially neutral objects, A and B, are rubbed together. Object A gains electrons. Which of the following is true about the charges of A and B? (A) A is positive, B is negative (B) A is negative, B is positive (C) A and B are both positive (D) A and B are both negative

3. A positively charged object is brought near a neutral conductor. What happens to the charges in the conductor? (A) Positive charges move toward the charged object. (B) Negative charges move toward the charged object. (C) Positive charges move away from the charged object. (D) No charges move within the conductor.

Free Response Question:

Two small spheres, each with a mass of 0.005 kg, are suspended from the same point by insulating threads of length 0.5 m. The spheres are given equal positive charges, and they are observed to be separated by a distance of 0.2 m. Assume the system is in equilibrium.

(a) Draw a free-body diagram for one of the spheres, labeling all forces acting on it. (b) Calculate the magnitude of the electrostatic force between the two spheres. (c) Calculate the charge on each sphere. (d) If the length of the threads is doubled, what will happen to the separation distance between the spheres? Explain your reasoning.

Scoring Breakdown:

(a) (3 points) - 1 point for tension force (T) pointing along the thread - 1 point for gravitational force (mg) pointing downward - 1 point for electrostatic force (Fe) pointing horizontally away from the other sphere

(b) (2 points) - 1 point for correctly using trigonometry to find the angle of the thread - 1 point for setting up and solving the equilibrium equation using the angle and mass

• $tan \theta = \frac{0.1}{0.5} = 0.2$
• $\theta = tan^{-1}(0.2) = 11.31^o$
• $F_e = mg \tan\theta = (0.005 \text{ kg})(9.8 \text{ m/s}^2)\tan(11.31^o) = 0.0098 N$

(c) (3 points) - 1 point for using Coulomb's law $F = k \frac{q_1 q_2}{r^2}$ - 1 point for correctly substituting values - 1 point for solving for q

• $0.0098 = (9 \times 10^9) \frac{q^2}{0.2^2}$
• $q = \sqrt{\frac{0.0098 \times 0.2^2}{9 \times 10^9}} = 2.09 \times 10^{-7} C$

(d) (2 points) - 1 point for stating that the separation distance will increase - 1 point for explaining that increasing the thread length will increase the angle between the threads, leading to a greater separation distance

Answer Key:

Multiple Choice:

1. (A)
2. (B)
3. (B)

#Final Exam Focus

Okay, you've made it this far! Here’s what to focus on for the exam:

• High-Priority Topics:

  • Conservation of charge
  • Calculating electric forces (Coulomb's Law)
  • Understanding charging methods (friction, contact, induction)
  • Grounding and its effects

• Common Question Types:

  • Multiple-choice questions testing conceptual understanding of charge transfer and conservation.
  • Free-response questions involving force calculations and charge distribution analysis.
  • Questions that combine electrostatics with other units, like mechanics (forces, equilibrium).

#Last-Minute Tips

• Review your notes: Focus on the key concepts and formulas.
• Practice, practice, practice: Work through as many practice problems as you can.
• Stay calm: You've prepared for this, trust your knowledge, and take deep breaths.

You’ve got this! Go ace that exam!