#AP Physics C: E&M - Magnetic Forces and Fields Study Guide 🚀

Hey there, future physicist! Let's get you prepped for the exam with a super-focused review of magnetic forces and fields. We'll break down the key concepts, nail down the formulas, and get you ready to tackle any question they throw your way. Let's do this!

#Forces on Wires in Magnetic Fields

#Force on a Current-Carrying Wire

• Remember how magnetic fields affect individual moving charges? Well, a wire with current is just a bunch of moving charges! 💡

• The force on a current-carrying wire in a magnetic field is given by:

  $$\vec{F} = I \vec{L} \times \vec{B}$$

  • $\vec{F}$ is the magnetic force vector
  • $I$ is the current in the wire
  • $\vec{L}$ is the length vector of the wire (direction is the same as the current)
  • $\vec{B}$ is the magnetic field vector

• The magnitude of the force is:

  $$F = ILB \sin(\theta)$$

  • $\theta$ is the angle between the wire and the magnetic field.

#Right-Hand Rule (RHR) for Wires

• Use the RHR to find the direction of the force:
  1. Thumb: Points in the direction of the current ($I$).
  2. Fingers: Point in the direction of the magnetic field ($B$).
  3. Palm: Points in the direction of the force ($F$).

#Example: Force on a Wire Segment

• Consider a wire with straight and curved sections in a magnetic field (pointing into the page).

• Straight Sections:
  • Force magnitude: $F_s = ILB$ (if the angle is 90 degrees)
  • Direction: Use RHR (force will be either up or down, depending on the current direction).
• Curved Sections:
  • Break into tiny dl segments. However, due to symmetry, the net horizontal force cancels out.
  • Focus on the vertical force components.

#Torque on a Current Loop 🚨

#Torque Basics

• Even though the net force on a closed loop in a magnetic field is zero, there can still be a net torque, causing the loop to rotate.

• Torque is a rotational force: $\tau = rF\sin(\theta)$ ...