Electromagnetic Induction (AP Physics C: E&M) — Math expr, Expr math (extended) Cheat Sheet

The core ideas of Electromagnetic Induction (AP Physics C: E&M) — Math expr, Expr math (extended) distilled into a single, scannable reference — perfect for review or quick lookup.

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Quick Reference

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Key Terms at a Glance

Electromagnetic Induction:The production of an EMF (and current in a closed circuit) by a change in magnetic flux through a loop.

Faraday s Law:$\mathcal{E}=-N\frac{d\Phi_B}{dt}$. The induced EMF equals the negative rate of change of total flux linkage.

Lenz s Law:The direction of the induced EMF opposes the change in flux that caused it, ensuring energy conservation.

Motional EMF:EMF generated by a conductor moving through a magnetic field: $\mathcal{E}=BLv$.

Inductance ($L$):Ratio of magnetic flux linkage to current. SI unit: henry (H). $1$ H $= 1$ Wb/A.

Henry (H):SI unit of inductance. A coil has $1$ H if $1$ A produces $1$ Wb of flux linkage.

Mutual Inductance ($M$):Measures how flux through one coil depends on current in another. $M_{12}=M_{21}$ by reciprocity.

Back-EMF:The self-induced EMF in a coil that opposes changes in current: $\mathcal{E}=-L\frac{dI}{dt}$.

RL Circuit:A circuit with a resistor and inductor in series. Time constant $\tau=L/R$ governs transient behavior.

Time Constant ($\tau$):For RL circuits, $\tau=L/R$. The time for current to reach $63\%$ (growth) or drop to $37\%$ (decay).

LC Circuit:An ideal inductor-capacitor circuit that oscillates at $\omega=1/\sqrt{LC}$ with no damping.

Displacement Current:$I_d=\varepsilon_0 d\Phi_E/dt$. A changing electric flux acts as a source of $\vec{B}$ in Maxwell s equations.

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

Eddy Current:Circulating current induced in a bulk conductor by a changing magnetic field. Causes resistive heating.

Maxwell s Equations:Four fundamental equations unifying electricity and magnetism: Gauss (E), Gauss (B), Faraday, Ampere-Maxwell.

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