#AP Physics 2: Unit 5 - Electromagnetism 🧲

Welcome to your ultimate Unit 5 study guide! This unit dives into the fascinating world of electromagnetism, a cornerstone of modern technology. Let's get started!

This unit constitutes approximately 10% of the AP exam, so it's crucial to master these concepts. Focus on understanding the relationships between electric and magnetic fields, and their applications.

#Electric Fields & Forces 🧙

This section builds upon concepts from Unit 3, particularly Coulomb's Law. If you need a refresher, revisit that material before proceeding.

#Electrostatic Force & Coulomb's Law

Coulomb's Law quantifies the force between two point charges:

$$F = k \frac{|q_1 q_2|}{r^2}$$

Where:

• $F$ is the electrostatic force
• $k$ is Coulomb's constant
• $q_1$ and $q_2$ are the magnitudes of the charges
• $r$ is the distance between the charges

• Electrostatic force is a fundamental force that governs the interactions of charged particles.
• Coulomb's Law is the mathematical expression of this force.

#Electric Fields

Every charged object creates an electric field around it. The field exerts a force on any other charge placed within it. Electric fields are represented by field lines, which are vectors that indicate the direction of the force on a positive test charge.

Key Rules for Drawing Electric Fields:

• Field lines originate from positive charges and terminate at negative charges.
• Field lines are always perpendicular to the surface of a charged conductor.
• Field lines never cross each other.
• The density of field lines indicates the strength of the field.

#Simple Fields 🌐

• Point Charges: Field lines radiate outward from positive charges and inward toward negative charges.

  

  Radial symmetry is key here.

• Two Point Charges: Field lines curve from the positive to the negative charge.

  

  Notice how the field lines never cross.

• Two Parallel Plates: The field is uniform between the plates, with lines going from positive to negative.

  

  The field is constant in magnitude and direction between the plates.

#Electric Field Strength

Electric field strength ($E$) is the force per unit charge experienced by a test charge in the field:

$$E = \frac{F}{q}$$

Where:

• $E$ is the electric field strength (V/m or N/C)
• $F$ is the electrostatic force (N)
• $q$ is the magnitude of the test charge (C)

We can also express the electric field due to a point charge $Q$:

$$E = k \frac{Q}{r^2}$$

#Practice Questions:

Practice Question

1. Multiple Choice:

   Three pairs of point charges are shown below. Rank the magnitude of the electrostatic force between each pair, from greatest to least.

   

   (A) A > B > C > D > E > F (B) C > D > A > B > E > F (C) C = D > A = B > E = F (D) A = B > C = D > E = F

   Answer: (C)

2. Multiple Choice:

   A test charge is placed at the center of a square with two other charges, as shown. What is the direction of the net force on the test charge?

   

   (A) Upward (B) Downward (C) Towards the bottom left corner (D) Towards the top right corner

   If the magnitude of force due to one of the charges is F, what is the net force on the test charge?

   (A) F (B) 2F (C) √2F (D) 4F

   Answer: (C) and (C)

3. Multiple Choice:

   Two pieces of tape are prepared. Tape 1 attracts an uncharged object. Tape 2 also attracts an uncharged object. Tape 1 repels tape 2. Which of the following is true about the charges on the tapes?

   

   (A) Tape 1 is positively charged, and Tape 2 is negatively charged. (B) Tape 1 is negatively charged, and Tape 2 is positively charged. (C) Both tapes are positively charged. (D) Both tapes are negatively charged.

   Answer: (B)

4. Free Response Question:

   A positive charge +Q is fixed at the origin. A small test charge +q is placed at position (x, 0). The electrostatic force on the test charge is measured to be F.

   (a) What is the direction of the electric field at the position of the test charge? (b) Express the electric field strength at the position of the test charge in terms of F and q. (c) If the test charge is moved to a position (2x,0), what is the new electrostatic force on it in terms of F? (d) If the test charge is replaced by a negative charge -q, what is the new direction of the force on it?

   Answer:

   (a) The electric field is directed radially away from the positive charge +Q, so it is in the positive x direction. (1 point) (b) $E = F/q$ (1 point) (c) The force is inversely proportional to the square of the distance. The new distance is 2x, so the new force is F/4. (2 points) (d) The force on the negative charge is in the opposite direction of the force on the positive charge. So, it is in the negative x direction. (1 point)

#Final Exam Focus 🎯

• High-Priority Topics: Electrostatic forces, electric fields, and their relationship. Pay close attention to how field lines are drawn and interpreted.
• Common Question Types: Problems involving forces between multiple charges, calculating electric field strength, and analyzing motion of charges in electric fields.
• Time Management: Quickly identify the type of problem and apply the relevant formulas. Practice vector addition for forces and fields.
• Common Pitfalls: Forgetting that forces and fields are vectors, confusing test charges with source charges, and not paying attention to the direction of forces and fields.

Good luck with your exam! You've got this! 💪