Jewelry Rings

Faraday’s law?

You hold a thin gold wedding ring with an inside radius of 1 cm, such that the plane of the ring is perpendicular to the Earth’s magnetic field. At your location it has strength 5.5×10−5 T. What is the emf induced in the ring if you turn it in one-tenth of a second to be parallel to the field (that is, you make the area vector of the ring perpendicular to the field) (V)?

Here’s my attempt:
E = ε/(2πr) = -(r/2)*(dB/dt) –> ε = -(r/2)*(dB/dt)*(2πr)
ε = -[(0.01m)/2] * [(5.5×10^-5T)/(0.1s)] * [2*π*(0.01m)]
…
ε = -1.73×10^-7 (T*m²)/s = -1.73×10^-7 V

Units conversion:
T*(m²/s) = {N/[(C/s)*m]}*{m²/s} = (N*m)/C = J/C = V

Dost thou concur?

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