#AP Physics C: E&M - Magnetism and Moving Charges ⚡

Hey there! Let's dive into the exciting world of magnetism and moving charges. This is a super important topic, so let's make sure you're feeling confident. We'll break it down step-by-step, so you'll be ready to ace this on the exam.

#Magnetic Fields of Moving Charges

#Single Moving Charge Field 🧲

• A single moving charge creates its own magnetic field. Think of it like a tiny magnet that only appears when the charge is in motion.

• Direction: Use the right-hand rule to find the magnetic field direction. Point your thumb in the direction of the charge's velocity, and your curled fingers will show the direction of the magnetic field lines.

• Strength: The magnetic field is strongest when the velocity and position vectors are perpendicular (90° angle) and weakens as the angle deviates from 90°.

  

  Caption: Magnetic field lines around a moving positive charge. Notice how the field is circular and the direction is determined by the right-hand rule.

#Force on Moving Charges in Magnetic Fields

#Cross-Product of Velocity and Field

• A magnetic field exerts a force on a moving charge. This force is what makes motors and other cool tech work!
• Force Calculation: The magnetic force is given by the equation: $$\vec{F}_{B} = q(\vec{v} \times \vec{B})$$
  • $\vec{F}_{B}$ is the magnetic force vector.
  • $q$ is the charge (positive or negative).
  • $\vec{v}$ is the velocity vector of the charge.
  • $\vec{B}$ is the magnetic field vector.
• The cross product means the force is perpendicular to both the velocity and the magnetic field. Use the right-hand rule again to figure out the direction of the force.

#Combined Electric and Magnetic Fields

• When both electric and magnetic fields are present, a charged particle feels both forces.
• Electric Force: $\vec{F}_{E} = q\vec{E}$ (force due to electric fiel...