Question

A wheel has \[10\] metallic spokes, each \[0.5\,\mathrm{m}\] long. It rotates at \[120\,\mathrm{rev/min}\] in a plane normal to Earth's horizontal magnetic field \[H_E=0.4\,\mathrm{G}\]. What is the induced EMF between the axle and rim?

Options

• \[\varepsilon\approx6.28\times10^{-4}\,\mathrm{V}\]

• \[\varepsilon\approx6.28\times10^{-6}\,\mathrm{V}\]

• \[\varepsilon\approx6.28\,\mathrm{V}\]

• \[\varepsilon\approx6.28\times10^{-5}\,\mathrm{V}\]

Answer 1

Use \[B=0.4\times10^{-4}\,\mathrm{T}\], \[\omega=4\pi\,\mathrm{rad/s}\], and \[R=0.5\,\mathrm{m}\]. Then \[\varepsilon=\frac{1}{2}B\omega R^2\approx6.28\times10^{-5}\,\mathrm{V}\].