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Unformatted text preview: ωt + α )ˆ z . Find the induced current density J f produced in the disc. Problem 4. 1. Use the analogy between Faraday’s law and Amp` ere’s law, together with the Biot-Savart law, to show that E ( r , t ) =-1 4 π ∂ ∂t ∫ B ( r ′ , t ) × ( r-r ′ ) | r-r ′ | 3 dτ ′ , (1) for induced electric ﬁelds. 1 2. Show that E =-∂ A ∂t , (2) where A is the vector potential. Check this result by taking the curl of both sides. Problem 5. An electromagnetic “eddy current” brake consists of a disc of conductivity σ and thickness d rotating about an axis passing through its center and normal to the surface of the disc. A uniform B is applied perpendicular to the plane of the disc over a small area a 2 located a distance ρ from the axis. Show that the torque tending to slow down the disc at the instant its angular speed is ω is given approximately by σωB 2 ρ 2 a 2 d . Problem 6. Griﬃths, Problem 7.7. Problem 7. Griﬃths, Problem 7.23. 2...
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- Spring '09