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 +qo at x = a and a small sphere carrying charge -qo 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-

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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
Transcribed Image Text: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
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