Q: Prove that the curl of a gradient is always zero. Check
Prove that the curl of a gradient is always zero. Check it for function (b) in Prob. 1.11.
See AnswerQ: A thin uniform donut, carrying charge Q and mass M ,
A thin uniform donut, carrying charge Q and mass M , rotates about its axis as shown in Fig. 5.64. (a) Find the ratio of its magnetic dipole moment to its angular momentum. This is called the gyromagn...
See AnswerQ: (a) Prove that the average magnetic field, over a
(a) Prove that the average magnetic ï¬eld, over a sphere of radius R, due to steady currents inside / where m is the total dipole moment of the sphere. Contrast the electrostatic resul...
See AnswerQ: (a) A phonograph record carries a uniform density of “
(a) A phonograph record carries a uniform density of “static electricity” σ . If it rotates at angular velocity ω, what is the surface current density K at a distance r from the center? (b) A uniforml...
See AnswerQ: A uniformly charged solid sphere of radius R carries a total charge
A uniformly charged solid sphere of radius R carries a total charge Q, and is set spinning with angular velocity ω about the z axis. (a) What is the magnetic dipole moment of the sphere? (b) Find the...
See AnswerQ: Using Eq. 5.88, calculate the average magnetic field
Using Eq. 5.88, calculate the average magnetic ï¬eld of a dipole over a sphere of radius R centered at the origin. Do the angular integrals ï¬rst. Compare your answer wit...
See AnswerQ: A thin glass rod of radius R and length L carries a
A thin glass rod of radius R and length L carries a uniform surface charge σ . It is set spinning about its axis, at an angular velocity ω. Find the magnetic ï¬eld...
See AnswerQ: For a configuration of charges and currents confined within a volume V
For a conï¬guration of charges and currents conï¬ned within a volume V, show that where p is the total dipole moment. [Hint: evaluate /
See AnswerQ: (a) Find the magnetic field at the center of a
(a) Find the magnetic ï¬eld at the center of a square loop, which carries a steady current I . Let R be the distance from center to side (Fig. 5.22). (b) Find the ï¬eld a...
See AnswerQ: Find the magnetic field at point P for each of the steady
Find the magnetic ï¬eld at point P for each of the steady current conï¬gurations shown in Fig. 5.23.
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