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Chapter 32: Q13P (page 967)
At what rate must the potential difference between the plates of a parallel-plate capacitor with a capacitance be changed to produce a displacement current of?
The rate of potential is .
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The magnetic field of Earth can be approximated as the magnetic field of a dipole. The horizontal and vertical components of this field at any distance r from Earth鈥檚 center are given by ,where lm is the magnetic latitude (this type of latitude is measured from the geomagnetic equator toward the north or south geomagnetic pole). Assume that Earth鈥檚 magnetic dipole moment has magnitude . (a) Show that the magnitude of Earth鈥檚 field at latitude lm is given by
(b) Show that the inclination of the magnetic field is related to the magnetic latitude by tan .A Rowland ring is formed of ferromagnetic material. It is circular in cross section, with an inner radius of and an outer radius of , and is wound with turns of wire. (a) What current must be set up in the windings to attain a toroidal field of magnitude ? (b) A secondary coil wound around the toroid has and resistance . If, for this value of , we have , how much charge moves through the secondary coil when the current in the toroid windings is turned on?
A magnetic compass has its needle, of mass and length, aligned with the horizontal component of Earth鈥檚 magnetic field at a place where that component has the value. After the compass is given a momentary gentle shake, the needle oscillates with angular frequency. Assuming that the needle is a uniform thin rod mounted at its center, find the magnitude of its magnetic dipole moment.
The magnitude of the magnetic dipole moment of Earth is . (a) If the origin of this magnetism were a magnetized iron sphere at the center of Earth, what would be its radius? (b) What fraction of the volume of Earth would such a sphere occupy? Assume complete alignment of the dipoles. The density of Earth鈥檚 inner core isrole="math" localid="1662967671929" .The magnetic dipole moment of an iron atom is . (Note:Earth鈥檚 inner core is in fact thought to be in both liquid and solid forms and partly iron, but a permanent magnet as the source of Earth鈥檚 magnetism has been ruled out by several considerations. For one, the temperature is certainly above the Curie point.)
Assume that an electron of mass mand charge magnitude emoves in a circular orbit of radius rabout a nucleus. A uniform magnetic fieldis then established perpendicular to the plane ofthe orbit. Assuming also that the radius of the orbit does not change and that the change in the speed of the electron due to fieldis small, find an expression for the change in the orbital magnetic dipole moment of the electron due to the field.
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