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Unformatted text preview: HW-8 1. Find the magnetic field at point P for each of the following steady current configurations. 2. Find the force on a square loop and a triangle near in infinite straight wire. J Jx . 3. A thick slab extending from z=-a to z=+a carries a uniform volume current density Find the magnetic field, as a function z, both inside and outside the slab. A ke (where k is a constant), in 4. What current density would produce the vector potential, cylindrical coordinates? 1 B is uniform, show that A (r B) works. 5. If 2 A B . A 0 That is, check that and 6. A thin uniform donut, carrying charge Q and mass M, rotates about its axis as shown below. (a) Find the ratio of its magnetic moment to its angular momentum, gyromagnetic ratio. (b) What’s the gyromagnetic ratio for a uniform spinning sphere? [This requires no new calculation; simply decompose the sphere into infinitesimal rings, and apply the result of part (a).] 1 (c) According to quantum mechanics, the angular momentum of a spinning electron is 2 , where is Planck’s constant. What, then, is the electron’s magnetic dipole moment? [This semiclassical value is actually off by a factor of almost exactly 2. Dirac’s relativistic electron theory got the 2 right, and Feymnman, Schwinger, and Tomonaga later calculated tiny further corrections. The determination of the electron’s magnetic dipole moment remains the finest achievement of quantum electrodynamics, and exhibits perhaps the most stunningly precise agreement between theory and the experiment in all e of physics. Incidentally, the quantity ( 2m ), where e is the charge of the electron and m is its mass, is called Bohr magneton.] This is called ...
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