AP Physics C: Electricity and Magnetism / Unit 12: Magnetic Fields and Electromagnetism
12.3 Magnetic Fields of Current-Carrying Wires and the Biot-Savart Law
Notes
$$d\vec B=\frac{\mu_0}{4\pi}\frac{I\,d\vec l\times\hat r}{r^2}$$
- Long straight wire: $\displaystyle B=\frac{\mu_0I}{2\pi r}$. Center of a loop: $\displaystyle B=\frac{\mu_0I}{2R}$.
- Force on a wire: $\vec F=I\vec L\times\vec B$.
Practice
The field at the center of a circular loop with current $I$, radius $R$:
From Biot-Savart.
Doubling the current in a long wire makes $B$:
$B\propto I$.
The direction of $B$ around a wire comes from:
Fingers curl with the field.
Ready for more? Take the Unit 12 test.