Inductance Practice Test

A solenoid with $N$ turns, length $\ell$, and cross-sectional area $A$ produces an approximately uniform internal field $B\approx \mu\frac{N}{\ell}I$, where $\mu=\mu_0\mu_r$ depends on the core material. The flux through each turn is $\Phi=BA$, so the flux linkage is $\lambda=N\Phi$. Using $\lambda=LI$, the solenoid inductance is $L\approx \mu\frac{N^2A}{\ell}$. Faraday’s law connects changing flux linkage to induced EMF: $\varepsilon=-\frac{d\lambda}{dt}=-L\frac{dI}{dt}$, consistent with Lenz’s law opposing current changes. Solenoids and inductors appear in relays and filters, where they resist rapid current variation. Explain the effect of changing current on the inductance of a solenoid.

In an AC circuit, an inductor of $L=0.50,\text{H}$ opposes changing current by inducing an EMF. Inductance links current to magnetic flux as $\lambda=N\Phi=LI$, and Faraday’s law gives $\varepsilon=-\frac{d\lambda}{dt}=-L\frac{dI}{dt}$. The inductor stores energy in its magnetic field with $U=\tfrac12 LI^2$, and an ideal inductor does not dissipate energy as heat. Self-inductance refers to a coil’s changing current producing a changing flux through the same coil, while mutual inductance refers to a changing current in one coil producing a changing flux through a nearby coil. Real inductors appear in filters and power supplies, where they smooth current changes by resisting rapid variations. Based on the passage, how does an inductor store energy in a magnetic field?