Problem 7.35 The preceding problem was an artificial model for the charging ca- pacitor, designed to avoid complications associated with the current spreading out over the surface of the plates. For a more realistic model, imagine thin wires that connect to the centers of the plates (Fig. 7.46a). Again, the current I is constant, the radius of the capacitor is a, and the separation of the plates is w <

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Chapter1: Units, Trigonometry. And Vectors
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Problem 7.35 The preceding problem was an artificial model for the charging ca-
pacitor, designed to avoid complications associated with the current spreading out
over the surface of the plates. For a more realistic model, imagine thin wires that
connect to the centers of the plates (Fig. 7.46a). Again, the current I is constant,
the radius of the capacitor is a, and the separation of the plates is w <<a. Assume
that the current flows out over the plates in such a way that the surface charge is
uniform, at any given time, and is zero at t = 0.
(a) Find the electric field between the plates, as a function of t.
(b) Find the displacement current through a circle of radius s in the plane mid-
way between the plates. Using this circle as your “Amperian loop,” and the flat
surface that spans it, find the magnetic field at a distances from the axis.
7.3 Maxwell's Equations
00
➢
พ
(a)
00
FIGURE 7.46
(b)
337
Transcribed Image Text:Problem 7.35 The preceding problem was an artificial model for the charging ca- pacitor, designed to avoid complications associated with the current spreading out over the surface of the plates. For a more realistic model, imagine thin wires that connect to the centers of the plates (Fig. 7.46a). Again, the current I is constant, the radius of the capacitor is a, and the separation of the plates is w <<a. Assume that the current flows out over the plates in such a way that the surface charge is uniform, at any given time, and is zero at t = 0. (a) Find the electric field between the plates, as a function of t. (b) Find the displacement current through a circle of radius s in the plane mid- way between the plates. Using this circle as your “Amperian loop,” and the flat surface that spans it, find the magnetic field at a distances from the axis. 7.3 Maxwell's Equations 00 ➢ พ (a) 00 FIGURE 7.46 (b) 337
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