#Magnetism and Current-Carrying Wires

Hey there, future AP Physics 2 master! Let's dive into the fascinating world of magnetism and current-carrying wires. Remember, it's all about the interplay between electricity and magnetism, and how they create forces and fields. Let's get started!

#Magnetic Field Produced by a Current-Carrying Wire

This is a core concept, and you'll see it pop up in multiple contexts. Make sure you understand both the field's direction and strength.

#Basics

• Current-carrying wires are like tiny magnets 🧲. They create magnetic fields around them.
• The magnetic field lines form concentric circles around the wire, perpendicular to it.
• The magnetic field vector is always tangent to these circles.
• There's no magnetic field component pointing towards, away from, or parallel to the wire itself.

#Field Strength

• The strength of the magnetic field depends on two main things:
  • Current (I): More current = stronger field (directly proportional).
  • Distance (r): Closer to the wire = stronger field (inversely proportional).

• Use this formula to calculate the magnetic field strength (B) near a long, straight wire:

  $$B=\frac{\mu_{0}}{2 \pi} \frac{I}{r}$$

  • $B$ = magnetic field strength (in Teslas, T)
  • $\mu_0$ = permeability of free space constant (a given constant, don't memorize it!)
  • $I$ = current in the wire (in Amperes, A)
  • $r$ = perpendicular distance from the wire (in meters, m)

#Direction of the Magnetic Field

• For a current loop, the magnetic field at its center points along the loop's axis. Use RHR1 to find the specific direction.
• When you have multiple current-carrying wires, find the net magnetic field at a location by adding the individual fields as vectors.

Practice Question

Multiple Choice Questions:

1. A long, straight wire carries a current of 2 A. What is the magnitude of the magnetic field at a distance of 1 cm from the wire? (Assume μ₀ = 4π × 10⁻⁷ T⋅m/A) (A) 4 × 10⁻⁵ T (B) 2 × 10⁻⁵ T (C) 4 × 10⁻⁷ T (D) 2 × 10⁻⁷ T

2. Two parallel wires carry currents in the same direction. What is the direction of the magnetic force on each wire? (A) Attractive (B) Repulsive (C) Zero (D) Depends on the magnitude of the current

Free Response Question:

A long, straight wire carries a current of 5.0 A in the +x direction. A second long, straight wire is parallel to the first and carries a current of 3.0 A in the -x direction. The wires are separated by a distance of 0.20 m. Calculate the magnitude and direction of the net magnetic field at a point midway between the two wires.

Scoring Guide:

• (2 points) Correctly calculate the magnetic field due to the first wire.
• (2 points) Correctly calculate the magnetic field due to the second wire.
• (2 points) Correctly add the two magnetic fields as vectors.
• (1 point) Correctly state the magnitude of the net magnetic field.
• (1 point) Correctly state the direction of the net magnetic field.

#Force on a Current-Carrying Wire in a Magnetic Field

#Basics

• A current-carrying wire placed in an external magnetic field experiences a force ⚡.
• The magnitude of this force depends on:
  1. Current (I): More current = more force (directly proportional).
  2. Length (ℓ): Longer wire in the field = more force (directly proportional).
  3. Magnetic Field (B): Stronger field = more force (directly proportional).
  4. Angle (θ): The angle between the current direction and the magnetic field direction.

#Calculating the Force

• Use this formula to calculate the magnetic force ($F_B$) on the wire:

  $$F_{B}=I \ell B \sin \theta$$

  • $F_B$ = magnetic force on the wire (in Newtons, N)
  • $I$ = current in the wire (in Amperes, A)
  • $\ell$ = length of the wire in the magnetic field (in meters, m)
  • $B$ = external magnetic field strength (in Teslas, T)
  • $\theta$ = angle between the current and the magnetic field

#Direction of the Magnetic Force

Practice Question

Multiple Choice Questions:

1. A wire carrying a current of 5 A is placed in a uniform magnetic field of 0.2 T. The length of the wire in the field is 0.5 m. If the wire is perpendicular to the magnetic field, what is the magnitude of the force on the wire? (A) 0.5 N (B) 0.2 N (C) 1 N (D) 0 N

2. A current-carrying wire is placed in a magnetic field. If the direction of the current is parallel to the magnetic field, what is the magnitude of the magnetic force on the wire? (A) Maximum (B) Minimum (C) Zero (D) Cannot be determined

Free Response Question:

A rectangular loop of wire with dimensions 10 cm by 20 cm carries a current of 2.0 A. It is placed in a uniform magnetic field of 0.5 T directed perpendicular to the plane of the loop. Calculate the magnitude of the magnetic force on each side of the loop. What is the net force on the loop?

Scoring Guide:

• (2 points) Correctly calculate the magnetic force on each side of the loop.
• (2 points) Correctly state that forces on opposite sides cancel each other.
• (1 point) Correctly state the net force on the loop.
• (1 point) Correctly state the direction of the force on each side.

#Final Exam Focus

#High-Priority Topics

• Magnetic Field of a Wire: Calculating field strength, determining direction using RHR1. * Force on a Wire: Calculating force magnitude and direction using RHR2. * Combining Concepts: Problems that require you to combine both concepts (e.g., finding the net force on a wire due to multiple magnetic fields).

#Common Pitfalls

#Last-Minute Tips

• Time Management: Don't spend too long on a single question. If you're stuck, move on and come back to it later.
• Show Your Work: Even if you don't get the final answer, you can get partial credit for showing your work and using the correct formulas.
• Draw Diagrams: Diagrams can help you visualize the problem and determine the direction of magnetic fields and forces.
• Stay Calm: You've got this! Take a deep breath and approach the exam with confidence.

Good luck, you're going to rock this exam! 🚀