Electrical Generators and Motors

A generator has a cell with 1000 circular loops of wire that each have a radius of 30 cm. They have a frequency of 60 Hz. The generator will create an rms (average) voltage of 100 V with a maximum electromotive force (emf) of 150 V. What is the magnitude of the magnetic field?


    • \varepsilon_{0}=150\ V
    • r=0.30\ m
    • N=1000
    • f=60\ Hz=60\ s^{-1}


    • B (magnetic field)

\varepsilon =N\cdot B\cdot A\cdot\omega\cdot sin(\omega t)

To maximize this equation, we must look at the sin(ωt) part.

Sin(x) can be at most equal to one.

\varepsilon_{0}=N\cdot B\cdot A\cdot \omega\cdot (1)

    • Angular frequency: \omega =2\pi f
    • Area: A=\pi r^2

\frac{\varepsilon_{0}}{N(\pi r^{2})(2\pi f)}=\frac{N\cdot B\cdot (\pi r^{2})(2\pi f)}{N(\pi r^{2})(2\pi f)}


B=\frac{150\ V}{2\pi^{2}(1000)(0.30\ m)^{2}(60\ s^{-1})}=(1.41\times 10^{-3}\frac{V\cdot s}{m^2})(\frac{1\ T}{1\ \frac{V\cdot s}{m^{2}}})

B=1.41\times 10^{-3}\ T