Magnetic Fields and Forces (AP Physics C: E&M) Cheat Sheet

The core ideas of Magnetic Fields and Forces (AP Physics C: E&M) distilled into a single, scannable reference — perfect for review or quick lookup.

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Quick Reference

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Magnetic Field ($\vec{B}$):A vector field produced by moving charges or currents that exerts forces on other moving charges. SI unit: tesla (T).

Biot-Savart Law:Gives the differential magnetic field $d\vec{B}$ produced by a current element $Id\vec{l}$ at a field point.

Ampere s Law:$\oint\vec{B}\cdotd\vec{l}=\mu_0 I_{enc}$. Relates the circulation of $\vec{B}$ to enclosed current; most useful with high symmetry.

Solenoid:A tightly wound helical coil carrying current. Produces a nearly uniform interior field $B=\mu_0 nI$.

Toroid:A doughnut-shaped coil. The field inside is $B=\frac{\mu_0 NI}{2\pi r}$; zero outside.

Lorentz Force:The total electromagnetic force on a charge: $\vec{F}=q(\vec{E}+\vec{v}\times\vec{B})$.

Tesla (T):SI unit of magnetic field. $1\;T = 1\;\frac{kg}{A\cdots^2}$.

Gauss (G):CGS unit of magnetic field. $1\;T = 10^4\;G$.

Cyclotron Motion:Circular motion of a charged particle in a uniform magnetic field with radius $r=mv/(qB)$.

Magnetic Flux ($\Phi_B$):The surface integral of $\vec{B}$ over an area. $\Phi_B=\int\vec{B}\cdotd\vec{A}$. SI unit: weber (Wb).

Weber (Wb):SI unit of magnetic flux. $1\;Wb = 1\;T\cdotm^2$.

Magnetic Dipole Moment:$\vec{\mu}=NIA\hat{n}$. Characterizes the strength and orientation of a current loop in a magnetic field.

Permeability of Free Space ($\mu_0$):$\mu_0=4\pi\times10^{-7}\;T\cdotm/A$. Fundamental constant in magnetostatics.

Right-Hand Rule:Curl fingers of right hand in direction of current; thumb points along $\vec{B}$ (for solenoid) or use cross-product rule for forces.

Hall Effect:A voltage develops perpendicular to both current and $\vec{B}$ in a conductor, allowing measurement of carrier sign and density.

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