Physics 2 · Unit 5 Magnetism · 14 min read · Updated 2026-05-11
Magnetic Fields Due to Currents — AP Physics 2
AP Physics 2 · Unit 5 Magnetism · 14 min read
1. Biot-Savart Law and Straight Wire Magnetic Fields★★☆☆☆⏱ 4 min
The Biot-Savart Law is the general rule for finding the magnetic field from any steady current distribution. It breaks total current into infinitesimal segments $Id\vec{l}$, each producing a small magnetic field $d\vec{B}$ at a point a distance $r$ from the segment.
Where $d\vec{l}$ points in the direction of conventional current, $\hat{r}$ is the unit vector from the current segment to the point of interest, and direction follows the right-hand rule for cross products. For an infinitely long straight wire, integrating Biot-Savart gives a simple magnitude formula:
B = \frac{\mu_0 I}{2\pi r}
Here $r$ is the perpendicular distance from the wire to the point of interest. Direction uses the right-hand grip rule: point your right thumb along conventional current, and your curled fingers follow the circular direction of magnetic field loops around the wire.
2. Magnetic Force Between Parallel Current-Carrying Wires★★★☆☆⏱ 3 min
Any current-carrying wire placed in an external magnetic field experiences a net magnetic force $F = BIL\sin\theta$, where $ heta$ is the angle between the current direction and the external magnetic field. If we have two parallel current-carrying wires, each wire produces a magnetic field that exerts a force on the other.
For two parallel wires of length $L$, carrying currents $I_1$ and $I_2$, separated by distance $d$, the magnetic field from Wire 1 at Wire 2 is $B_1 = \frac{\mu_0 I_1}{2\pi d}$, and this field is perpendicular to Wire 2 so $
\sin\theta = 1$. Substituting gives the net force:
F = \frac{\mu_0 I_1 I_2 L}{2\pi d}
The direction rule is simple: parallel currents attract, opposite currents repel. This is the basis for the SI definition of the ampere, though AP Physics 2 does not require you to memorize this definition.
3. Ampère's Law and Magnetic Fields from Solenoids★★★☆☆⏱ 4 min
Ampère's Law is a simpler alternative to the Biot-Savart Law for current distributions with high symmetry. Ampère's Law states that the line integral of the magnetic field around any closed loop (called an Amperian loop) equals $
\mu_0$ times the net current enclosed by the loop:
To use Ampère's Law effectively, you choose an Amperian loop that matches the symmetry of the magnetic field, so that $B$ is constant and parallel to the loop everywhere it is non-zero. One of the most common applications of Ampère's Law in AP Physics 2 is finding the magnetic field inside an ideal solenoid.
An ideal solenoid is a long coil of tightly wound turns of wire carrying current $I$. The magnetic field is uniform and parallel to the solenoid axis inside the coil, and zero outside the coil. If $n = N/L$ is the number of turns per unit length, Ampère's Law simplifies to give:
B = \mu_0 n I
Direction of the magnetic field inside a solenoid uses a right-hand grip rule: curl your right fingers around the solenoid in the direction of current flow, and your thumb points in the direction of the magnetic field along the solenoid axis.
4. AP Style Practice Problems★★★★☆⏱ 3 min
Common Pitfalls
Why: Many students learn electron flow first in introductory physics and forget AP uses conventional current for all rules
Why: Students memorize the formula incorrectly, mixing up notation from different sources
Why: Students confuse finite real solenoids with the ideal approximation used in AP Physics 2
Why: Students confuse the force rule for currents with the force rule for static electric charges
Why: Students misapply the formula to points off the perpendicular axis and take the wrong distance