#AP Physics C: E&M - Magnetic Forces on Conductors Study Guide

Hey there, future physics pro! Let's break down magnetic forces on conductors. This is a big topic, but we'll make it super clear and easy to remember. Get ready to ace that exam!

#Magnetic Forces on Conductors in Magnetic Fields

#Introduction

• Magnetic forces on conductors happen when induced currents flow in a conductive loop. These currents cause charge carriers to move, and they experience forces from pre-existing magnetic fields.
• The strength of these forces depends on things like the loop's size, the magnetic field's strength, and the relative velocity between the loop and the field.
• Understanding this is key to analyzing how conducting loops move in magnetic fields and using Newton's second law to predict their behavior.

#Force on Conductors in Magnetic Fields

#Magnetic Force on Induced Currents

• Induced currents in conductive loops feel magnetic forces from existing magnetic fields, making the charge carriers move. 🏃‍♂️

• Calculate the magnetic force using this equation:

  $$\vec{F}_{B}=\int I(\vec{d} \times \vec{B})$$

  • $\vec{F}_{B}$ is the magnetic force vector.
  • $I$ is the induced current.
  • $\vec{d}$ is the tiny displacement vector of the conductor.
  • $\vec{B}$ is the magnetic field vector.

• Magnetic forces only affect the parts of the loop that are inside the external magnetic field.

• These forces can cause:

  • Translational acceleration: The loop moves in a straight line.
  • Rotational acceleration: The loop spins or rotates.

#Partial Field Interactions

• The force on a loop depends on:
  • Induced current: How quickly the magnetic flux changes through the loop.
  • Loop resistance: Affects how much current flows.
  • Loop velocity: How fast the...