The magnitude of emf generated between the ends of the rod is μ 0 v I l 2 π r .

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A conducting rod moves with a constant velocity in a direction perpendicular to a long, straight wire carrying a current I as shown in Figure P30.40. Show that the magnitude of the emf generated between the ends of the rod isChapter 30, Problem 40AP, A conducting rod moves with a constant velocity in a direction perpendicular to a long, straight , example 1In this case, note that the emf decreases with increasing r as you might expect.Figure P30.40Chapter 30, Problem 40AP, A conducting rod moves with a constant velocity in a perpendicular to a long, straight , example 2

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Chapter 30, Problem 40AP

To determine

To show: The magnitude of emf generated between the ends of the rod is μ0vIl2πr .

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A conducting rod moves with a constant velocity in a direction perpendicular to a long, straight wire carrying a current I as shown in Figure P30.40. Show that the magnitude of the emf generated between the ends of the rod isChapter 30, Problem 40AP, A conducting rod moves with a constant velocity in a direction perpendicular to a long, straight , example 1In this case, note that the emf decreases with increasing r as you might expect.Figure P30.40Chapter 30, Problem 40AP, A conducting rod moves with a constant velocity in a perpendicular to a long, straight , example 2

30. A short wire runs along an x axis from x = a to x = -a (Figure P30.30). At t = 0, there is a small sphere carry- ing charge +9o at x = a and a small sphere carrying charge -9o at x = -a. As the spheres discharge and a current is established in the wire, show that, for t>0, the generalized form of Ampère's law (Eq. 30.13) and the Biot-Savart law (Eq. 28.12) give the same result for the magnitude of the mag- netic field a distance b up the y axis. (Hint: Obtain the elec- tric flux through a circular disk in the yz plane, centered at the origin. Because the electric field is not constant over the surface of the disk, you must divide the disk into a nested set of rings of various radii and integrate. A representative ring should have radius r and radial extent dr.) •.. Figure P30.30 b -90

b. It has been suggested that birds might use the EMF induced between their wing tips by the earth's magnetic field as a means of helping them navigate during migration. What EMF would be induced for a Canada goose with a wingspread of 1.5 m flying 10 m/s in a region where the vertical component of the earth's field is 30 µT?