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Chapter 7: Q9P (page 311)
An infinite number of different surfaces can be fit to a given boundary line, and yet, in defining the magnetic flux through a loop, da, I never specified the particular surface to be used. Justify this apparent oversight.
It is necessary to specify particular surface oversight.
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Suppose the circuit in Fig. 7.41 has been connected for a long time when suddenly, at time , switch S is thrown from A to B, bypassing the battery.
Notice the similarity to Eq. 7.28-in a sense, the rectangular toroid is a short coaxial cable, turned on its side.
(a) What is the current at any subsequent time t?
(b) What is the total energy delivered to the resistor?
(c) Show that this is equal to the energy originally stored in the inductor.
A square loop of wire, with sides of length a , lies in the first quadrant of the xy plane, with one comer at the origin. In this region, there is a nonuniform time-dependent magnetic field (where k is a constant). Find the emf induced in the loop.
Question: A rare case in which the electrostatic field E for a circuit can actually be calculated is the following: Imagine an infinitely long cylindrical sheet, of uniform resistivity and radius a . A slot (corresponding to the battery) is maintained at , and a steady current flows over the surface, as indicated in Fig. 7.51. According to Ohm's law, then,
Figure 7.51
(a) Use separation of variables in cylindrical coordinates to determine inside and outside the cylinder.
(b) Find the surface charge density on the cylinder.
An alternating current flows down a long straight wire, and returns along a coaxial conducting tube of radius a.
(a) In what direction does the induced electric field point (radial, circumferential, or longitudinal)?
(b) Assuming that the field goes to zero as , find
A circular wire loop (radius, resistance) encloses a region of uniform magnetic field,, perpendicular to its plane. The field (occupying the shaded region in Fig. 7.56) increases linearly with time. An ideal voltmeter (infinite internal resistance) is connected between pointsand.
(a) What is the current in the loop?
(b) What does the voltmeter read? [Answer: ]
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