Q: What current density would produce the vector potential, A=k
What current density would produce the vector potential, A=k φˆ (where k is a constant), in cylindrical coordinates?
See AnswerQ: If B is uniform, show that / works
If B is uniform, show that / works. That is, check that / Is this result unique, or are there other functions with the same divergence and curl?
See AnswerQ: (a) By whatever means you can think of (short
(a) By whatever means you can think of (short of looking it up), find the vector potential a distance s from an infinite straight wire carrying a current I . Check that ∇ · A = 0 and ∇ × A = B. (b) Find...
See AnswerQ: Find the vector potential above and below the plane surface current in
Find the vector potential above and below the plane surface current in Ex. 5.8.
See AnswerQ: (a) Check that Eq. 5.65 is consistent
(a) Check that Eq. 5.65 is consistent with Eq. 5.63, by applying the divergence. (b) Check that Eq. 5.65 is consistent with Eq. 5.47, by applying the curl. (c) Check that Eq. 5.65 is consistent with E...
See AnswerQ: Suppose you want to define a magnetic scalar potential U (Eq
Suppose you want to deï¬ne a magnetic scalar potential U (Eq. 5.67) in the vicinity of a current-carrying wire. First of all, you must stay away from the wire itself / but thatâ&...
See AnswerQ: In 1897, J. J. Thomson “discovered” the
In 1897, J. J. Thomson “discovered” the electron by measuring the charge-to-mass ratio of “cathode rays” (actually, streams of electrons, with charge q and mass m) as follows: (a) First he passed the...
See AnswerQ: (a) Check product rule (iv) (by calculating
(a) Check product rule (iv) (by calculating each term separately) for the functions A = x xˆ + 2y yˆ + 3z zˆ; B = 3y xˆ − 2x yˆ. (b) Do the same for product rule (ii). (c) Do the same for rule (vi)....
See AnswerQ: Use the results of Ex. 5.11 to find the
Use the results of Ex. 5.11 to find the magnetic field inside a solid sphere, of uniform charge density ρ and radius R, that is rotating at a constant angular velocity ω.
See AnswerQ: (a) Complete the proof of Theorem 2, Sect.
(a) Complete the proof of Theorem 2, Sect. 1.6.2. That is, show that any diver genceless vector field F can be written as the curl of a vector potential A. What you have to do is find Ax , Ay , and Az s...
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