Alternator: from peak EMF to angular frequency

Problem

An alternator produces a maximum EMF $\mathcal{E}_0 = 311 \ \mathrm{V}$ with a coil of area $A = 0{,}020 \ \mathrm{m^2}$, $N = 200$ turns, immersed in a field $B = 0{,}50 \ \mathrm{T}$. At what angular frequency $\omega$ does the coil rotate? And at how many revolutions per minute?

Coil rotating with angular frequency $\omega$ in a uniform magnetic field.

Solution

The maximum EMF of a rotating loop is $\mathcal{E}_0 = N B A\,\omega$. Solving for the angular frequency: $\omega = \frac{\mathcal{E}_0}{N B A} = \frac{311}{200 \cdot 0{,}50 \cdot 0{,}020} = \frac{311}{2{,}0} \approx \ev{156 \ \mathrm{rad/s}}$ The corresponding frequency: $f = \frac{\omega}{2\pi} = \frac{156}{6{,}28} \approx \ev{24{,}8 \ \mathrm{Hz}}$ Revolutions per minute: $n = f \cdot 60 \approx 24{,}8 \cdot 60 \approx \ev{1485 \ \mathrm{rpm}}$

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Topics: Induzione elettromagnetica Concepts: Legge di Faraday-Neumann-Lenz · Corrente alternata · Forza elettromotrice