Physics 2 · Unit 5: Magnetism and Electromagnetic Induction · 14 min read · Updated 2026-05-11
Magnetic Systems — AP Physics 2
AP Physics 2 · Unit 5: Magnetism and Electromagnetic Induction · 14 min read
1. Magnetic Dipole Moment★★☆☆☆⏱ 4 min
All magnetic behavior arises from magnetic dipoles, the fundamental building blocks of magnetism with no isolated magnetic monopoles. Magnetic dipole moment is a vector quantity that describes the magnetic strength and orientation of any magnetic system, from permanent bar magnets to current-carrying coils. For a flat, N-turn current-carrying coil with current $I$ and enclosed area $A$, the magnitude is given by:
\mu = N I A
The direction of $\vec{\mu}$ follows the right-hand rule for current loops: curl the fingers of your right hand along the current direction, and your thumb points in the direction of $\vec{\mu}$. Dipole moment is an intrinsic property of the system—it *does not depend* on any external magnetic field.
2. Torque on a Magnetic Dipole in a Uniform Field★★★☆☆⏱ 4 min
When a magnetic dipole is placed in a uniform external magnetic field, the net force on the dipole is always zero (forces on opposite sides of the dipole cancel out). However, there is a net torque that acts to align $\vec{\mu}$ with the external field $\vec{B}$. The vector formula for torque is:
\vec{\tau} = \vec{\mu} \times \vec{B}
The magnitude of torque is $\tau = \mu B \sin\theta$, where $\theta$ is the angle *between $\vec{\mu}$ and $\vec{B}$*. Torque is maximum when $\theta = 90^\circ$ and zero when the dipole is aligned or anti-aligned with the field. This torque is the operating principle of electric motors.
3. Potential Energy and Force on Magnetic Dipoles★★★☆☆⏱ 4 min
Since torque does work to rotate a dipole into alignment with an external field, we can define a potential energy for the dipole-field system, with zero potential energy defined at $\theta = 90^\circ$. The formula is:
U = -\vec{\mu} \cdot \vec{B} = -\mu B \cos\theta
Potential energy is minimized ($U = -\mu B$) when $\theta = 0^\circ$ (aligned, stable equilibrium) and maximized ($U = +\mu B$) when $\theta = 180^\circ$ (anti-aligned, unstable equilibrium). In uniform fields net force is zero, but in non-uniform fields aligned dipoles are pulled toward regions of stronger magnetic field.
4. AP-Style Concept Check★★★★☆⏱ 6 min
Common Pitfalls
Why: AP questions intentionally give the plane angle to test student understanding of what $\theta$ describes, and many students misinterpret the definition.
Why: Students confuse torque and force, and incorrectly generalize the non-uniform field force rule to all cases.
Why: The negative sign is easy to drop when memorizing, and students mix up magnetic potential energy with other forms of potential energy.
Why: Students mix up intrinsic properties of the dipole with interaction properties between the dipole and the field.
Why: Students confuse the multiple right-hand rules used in magnetism.