Q: Suppose you wanted to find the field of a circular loop (
Suppose you wanted to ï¬nd the ï¬eld of a circular loop (Ex. 5.6) at a point r that is not directly above the center (Fig. 5.60). You might as well choose your axes so th...
See AnswerQ: (a) If it is uniformly distributed over the surface,
(a) If it is uniformly distributed over the surface, what is the surface current density K ? (b) If it is distributed in such a way that the volume current density is inversely proportional to the dis...
See AnswerQ: Magnetostatics treats the “source current” (the one that sets
Magnetostatics treats the “source current†(the one that sets up the ï¬eld) and the “recipient current†(the one...
See AnswerQ: Consider a plane loop of wire that carries a steady current I
Consider a plane loop of wire that carries a steady current I ; we want to calculate the magnetic ï¬eld at a point in the plane. We might as well take that point to be the origin (it co...
See AnswerQ: (a) One way to fill in the “missing link
(a) One way to ï¬ll in the “missing link†in Fig. 5.48 is to exploit the analogy between the deï¬ning equations for and Maxwellâ...
See AnswerQ: Another way to fill in the “missing link” in Fig
Another way to ï¬ll in the “missing link†in Fig. 5.48 is to look for a magnetostatic analog to Eq. 2.21. The obvious candidate would be / (a) Test...
See AnswerQ: (a) Construct the scalar potential U(r) for
(a) Construct the scalar potential U(r) for a “pure” magnetic dipole m. (b) Construct a scalar potential for the spinning spherical shell (Ex. 5.11). [Hint: for r > R this is a pure dipole field, as yo...
See AnswerQ: Just as ∇ · B = 0 allows us to express B
Just as ∇ · B = 0 allows us to express B as the curl of a vector potential (B = ∇ × A), so ∇ · A = 0 permits us to write A itself as the curl of a “higher” potential: A = ∇ × W. (And this hierarchy ca...
See AnswerQ: Prove the following uniqueness theorem: If the current density J is
Prove the following uniqueness theorem: If the current density J is specified throughout a volume V, and either the potential A or the magnetic field B is specified on the surface S bounding V, then the...
See AnswerQ: A magnetic dipole / is situated at the origin
A magnetic dipole / is situated at the origin, in an otherwise uniform magnetic field / Show that there exists a spherical surface, centered at the origin, through which no magnetic field lines pass....
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