AP Physics – Electric Charge and Coulomb’s Law

AP Physics – Electric Charge and Coulomb’s Law

AP Physics: Electric Charge and Coulomb’s Law – Exam-Ready Study Guide

What This Is

Electric charge is the fundamental property of matter that causes it to experience a force when placed in an electric field. Coulomb’s Law quantifies the force between two point charges, forming the foundation for understanding electric fields, circuits, and even atomic structure. This topic appears on ~10-15% of the AP Physics exam (both multiple-choice and FRQs), often paired with electric fields or potential energy. Real-world example: Static cling in laundry (opposite charges attract) or the spark when you touch a doorknob after shuffling your feet (charge transfer via friction).

Key Terms & Concepts

• Electric charge (q or Q): A property of matter that causes it to experience a force in an electric field. Measured in coulombs (C). Protons (+e = +1.6 × 10?¹? C), electrons (-e = -1.6 × 10?¹? C).
• Conservation of charge: The total charge in an isolated system remains constant (charge can’t be created/destroyed, only transferred).
• Conductors vs. insulators:
• Conductors (e.g., metals) allow charge to move freely.
• Insulators (e.g., rubber, glass) restrict charge movement.
• Charging by conduction: Transferring charge by direct contact (e.g., rubbing a balloon on hair).
• Charging by induction: Redistributing charge in a neutral object by bringing a charged object nearby (no contact).
• Coulomb’s Law: The force between two point charges is: [ F = k \frac{|q_1 q_2|}{r^2} ]
• F = electrostatic force (N)
• k = Coulomb’s constant (8.99 × 10? N·m²/C²)
• q?, q? = charges (C)
• r = distance between charges (m)
• Superposition principle: The net force on a charge is the vector sum of forces from all other charges.
• Electric field (E): Force per unit charge experienced by a test charge: [ E = \frac{F}{q} = k \frac{|Q|}{r^2} ]
• E = electric field (N/C)
• Q = source charge (C)
• Test charge: A small positive charge (q) used to measure electric fields (doesn’t affect the field itself).

Step-by-Step: Solving Coulomb’s Law Problems

1. Draw a diagram: Sketch the charges, distances, and force directions (like charges repel; opposites attract).
2. Label knowns/unknowns: Identify given values (q?, q?, r, F) and what you’re solving for.
3. Apply Coulomb’s Law: Plug values into ( F = k \frac{|q_1 q_2|}{r^2} ). Use absolute values for q? and q? (force magnitude is always positive).
4. Vector addition (if multiple charges): Break forces into x/y components, sum them, then find the resultant force.
5. Check units: Ensure charges are in coulombs (C), distances in meters (m), and force in newtons (N).
6. Answer the question: If asked for direction, specify (e.g., "to the right" or "120° from the +x-axis").

Example: Two +3 µC charges are 0.5 m apart. What’s the force on one charge? - ( q_1 = q_2 = 3 \times 10^{-6} ) C - ( r = 0.5 ) m - ( F = (8.99 \times 10^9) \frac{(3 \times 10^{-6})^2}{(0.5)^2} = 0.324 ) N (repulsive).

Common Mistakes

• Mistake: Forgetting to convert microcoulombs (µC) to coulombs (C). Correction: 1 µC = 1 × 10 C. Always convert before plugging into formulas.

• Mistake: Ignoring vector directions (e.g., adding forces as scalars). Correction: Forces are vectors! Draw arrows and use trigonometry for angles.

• Mistake: Using the wrong sign for charges in Coulomb’s Law. Correction: The formula uses absolute values for magnitude. Direction is determined by charge signs (like repels like).

• Mistake: Confusing electric field (E) with force (F). Correction: ( E = \frac{F}{q} ). Field is force per unit charge; force depends on the test charge.

• Mistake: Assuming charges are point charges when they’re not (e.g., charged spheres with radius). Correction: For spheres, use the center-to-center distance (r) if charges are uniformly distributed.

AP Exam Insights

1. FRQ Hotspot: Expect a force vs. distance graph (Coulomb’s Law is inverse-square) or a problem with 3+ charges (superposition).
2. Multiple-Choice Trap: Questions may give charges in nano-/microcoulombs or distances in cm/mm—convert first!
3. Tricky Distinction: Electric field (E) vs. electric force (F):
4. E is a property of space (N/C).
5. F depends on the test charge (N).
6. Lab-Based FRQ: You might be asked to design an experiment to measure charge (e.g., using a known charge and Coulomb’s Law).

Quick Check Questions

1. MCQ: Two identical charges are 0.2 m apart. If the distance is increased to 0.4 m, the force between them: (A) Doubles (B) Halves (C) Decreases to 1/4 (D) Increases by 4× Answer: (C) Decreases to 1/4 (inverse-square law: ( F \propto \frac{1}{r^2} )).

2. FRQ: A +5 µC charge is 0.3 m from a -2 µC charge. Calculate the force on the -2 µC charge. Answer: ( F = (8.99 \times 10^9) \frac{(5 \times 10^{-6})(2 \times 10^{-6})}{(0.3)^2} = 0.999 ) N, attractive (toward the +5 µC charge).

3. MCQ: Which of the following will not change the electric force between two charges? (A) Doubling both charges (B) Halving the distance (C) Placing the charges in water (dielectric) (D) Changing the sign of one charge Answer: (D) Changing the sign (magnitude of force stays the same; only direction changes).

Last-Minute Cram Sheet

1. Coulomb’s Law: ( F = k \frac{|q_1 q_2|}{r^2} ) (k = 8.99 × 10? N·m²/C²).
2. 1 µC = 1 × 10 C Convert units!
3. Like charges repel; opposites attract.
4. Electric field (E): ( E = \frac{F}{q} = k \frac{|Q|}{r^2} ) (N/C).
5. Superposition: Net force = vector sum of individual forces.
6. Conductors allow charge flow; insulators don’t.
7. Charging by induction requires no contact (e.g., grounding).
8. Inverse-square law: Force-1/r².
9. Test charge is small and positive (doesn’t affect the field).
10. Direction matters! Draw force arrows before calculating.