OpenStax University Physics/E&M/Inductance

$ℰ\mathrm{\&}ℳ$ (Vol. 2):Template:Spaces 5:Electric Charges and FieldsTemplate:Spaces 6:Gauss's LawTemplate:Spaces 7:Electric PotentialTemplate:Spaces 8:CapacitanceTemplate:Spaces 9:Current and ResistanceTemplate:Spaces 10:Direct-Current CircuitsTemplate:Spaces 11:Magnetic Forces and FieldsTemplate:Spaces 12:Sources of Magnetic FieldsTemplate:Spaces 13:Electromagnetic InductionTemplate:Spaces 14:InductanceTemplate:Spaces 15:Alternating-Current CircuitsTemplate:Spaces 16:Electromagnetic Waves

Chapter 14

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For quiz at QB/d_cp2.14

Template:Colbegin Unit of inductance = Henry (H)=1V·s/A

Mutual inductance: $M\frac{d{I}_2}{dt}=N_1\frac{d{\mathrm{\Phi }}_{12}}{dt}=-{\epsilon }_1$ where ${\mathrm{\Phi }}_{12}$=flux through 1 due to current in 2. Reciprocity: $M\frac{d{I}_1}{dt}=-{\epsilon }_2$

Self-inductance: $N{\mathrm{\Phi }}_m=LI\to \epsilon =-L\frac{dI}{dt}$

$L_{\text{solenoid}}\approx {\mu }_0{N}^{2}A\ell$, $L_{\text{toroid}}\approx \frac{{\mu }_0{N}^{2}h}{2\pi }\ln \frac{R_2}{R_1}$, Stored energy=$\frac{1}{2}L{I}^2$

$I(t)=\frac{\epsilon }{R}(1-e^{-t/\tau })$ in LR circuit where $\tau =L/R$.

$q(t)=q_0\cos (\omega t+\varphi )$ in LC circuit where $\omega =\sqrt{\frac{1}{LC}}$ Template:Colend