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

Hey there! Let's get you totally prepped for the E&M exam. This guide is designed to be your go-to resource, especially the night before the test. We'll break down the concepts, highlight the key points, and make sure you're feeling confident and ready to rock!

#Magnetic Fields of Current-Carrying Wires

#Biot-Savart Law

• The Biot-Savart law is your starting point for understanding how currents create magnetic fields. It's all about calculating the magnetic field generated by a tiny segment of a wire carrying current. 💡
• Formula: $$d \vec{B}=\frac{\mu_{0}}{4 \pi} \frac{I(d\vec{\ell} \times \hat{r})}{r^{2}}$$
• Where:
  • $\mu_0$ is the permeability of free space (a constant).
  • $I$ is the current in the wire.
  • $d\vec{\ell}$ is a small length vector of the wire.
  • $\hat{r}$ is the unit vector from the wire to the point where you're calculating the field.
  • $r$ is the distance from the wire segment to the point.

- **Circular Loop:** At the center of a circular loop, the magnetic field is: - $$B\_{\text {center of loop }}=\frac{\mu\_{0} I}{2 R}$$ - $R$ is the radius of the loop. -

#Magnetic Field Vectors

• Visualize the magnetic field as concentric circles around a wire. 🌀
• The magnetic field vectors are always tangent to these circles.
• Key Point: They never point towards, away from, or parallel to the wire. This is a crucial difference from electric fields.
• The direction of the magnetic field is determined by the Right-Hand Rule:
  • Point your thumb in the direction of the current.
  • Your fingers curl in the direction of the magnetic field. 🖐️