Ranking EMF from varying fluxes

Problem

Three identical loops are subject to fluxes that vary linearly in time:

• A: $\Phi$ increases from $0$ to $0{,}1 \ \mathrm{Wb}$ in $1 \ \mathrm{s}$;
• B: $\Phi$ increases from $0$ to $0{,}2 \ \mathrm{Wb}$ in $4 \ \mathrm{s}$;
• C: $\Phi$ decreases from $0{,}2$ to $0 \ \mathrm{Wb}$ in $1 \ \mathrm{s}$.

Rank the magnitudes of the induced electromotive forces from smallest to largest.

Solution

The magnitude of the EMF depends only on the rate of change of the flux: $|\mathcal{E}| = \left|\dfrac{\Delta\Phi}{\Delta t}\right|$. $\begin{aligned} |\mathcal{E}_A| &= \frac{0{,}1}{1} = 0{,}10 \ \mathrm{V} \\ |\mathcal{E}_B| &= \frac{0{,}2}{4} = 0{,}05 \ \mathrm{V} \\ |\mathcal{E}_C| &= \frac{0{,}2}{1} = 0{,}20 \ \mathrm{V} \end{aligned}$ Increasing order (from smallest to largest): $\ev{|\mathcal{E}_B| < |\mathcal{E}_A| < |\mathcal{E}_C|}$ The direction (increase or decrease) only changes the sign, not the magnitude.

Collegamenti

Argomenti: Electromagnetic induction Concetti: Faraday-Neumann-Lenz law Competenze: Ranking reasoning · Flux balance