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Questions
Chapter 32
5. The induced magnetic field at radial distance 6.0 mm from the central axis of a circular
parallel-plate capacitor is 2.0 × 10-7 T. The plates have radius 3.0 mm. At what rate dE/dt
is the electric field between the plates changing?
7. Suppose that a parallel-plate capacitor has circular plates with radius R = 30 mm and a
plate separation of 5.0 mm. Suppose also that a sinusoidal potential difference with a
maximum value of 150 V and a frequency of 60 Hz is applied across plates; that is,
V = (150 V) sin[2π(60 Hz)t].
(a) Find Bmax(R), the maximum value of the induced magnetic field that occurs at r = R.
(b) Plot Bmax(r) for 0 < r < 10 cm.
14. A parallel-plate capacitor with circular plates of radius 0.10 m is being discharged. A
circular loop of radius 0.20 m is concentric with the capacitor and halfway between
plates. The displacement current through the loop is 2.0 A. At what rate is the electric
field between the plates changing?
23. Uniform displacement-current density. Figure 32-29 shows a circular region of radius
R = 3.00 cm in which a displacement current is directed out of the page. The
displacement current has a uniform density of magnitude Jd = 6.00 A/m2. What is the
magnitude of the magnetic field due to the displacement current at radial distances (a)
2.00 cm and (b) 5.00 cm?
28. Assume the average value of the vertical component of Earth’s magnetic field is 43
µT (downward) for all of Arizona, which has an area of 2.95 × 105 km2. What then are
the (a) magnitude and (b) direction (inward or outward) of the net magnetic flux through
the rest of Earth’s surface (the entire surface excluding Arizona)?
67. Earth has a magnetic dipole moment of 8.0 × 1022 J/T. (a) What current would have to
be produced in a single turn of wire extending around Earth at its geomagnetic equator if
we wished to set up such a dipole? Could such an arrangement be used to cancel out
Earth’s magnetism (b) at points in space well above Earth’s surface or (c) on Earth’s
surface?
72. Use the results displayed in Problem 71 to predict the (a) magnitude and (b)
inclination of Earth’s magnetic field at the geomagnetic equator, the (c) magnitude and
(d) inclination at geomagnetic latitude 60.0º, and the (e) magnitude and (f) inclination at
the north geomagnetic pole.
73. Using the approximations given in Problem 71, find (a) the altitude above Earth’s
surface where the magnitude of its magnetic field is 50.0% of the surface value at the
same latitude; (b) the maximum magnitude of the magnetic field at the core-mantle
boundary, 2900 km below Earth’s surface; and the (c) magnitude and (d) inclination of
Earth’s magnetic field at the north geographic pole. (e) Suggest why the values you
calculated for (c) and (d) differ from measured values.