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Consider an infinitely long straight wire with current I. Lets take the direction of the wire as the z-axis. Current is flowing in the positive z-direction. We already know the magnetic field. Find a vector potential for the case. Use the Coulomb gauge. 6. 7. For the example 1 of Chapter 6 in the textbook, obtain the magnetic field outside of the sphere.

of a polarized object was the same as that of a bound volume charge pV. plus a bound surface charge σι, P-i. Example 6.1. Find the magnetic field of a uniformly magnetized sphere. Solution Choosing the z axis along the direction of M (Fig. 6.12), we have FIGURE 6.12

Chapter 6 Magnetic Fields in Matter Now, a rotating spherical shell, of uniform surface charge σ , corresponds to a surface current density It follows, therefore, that the field of a uniformly magnetized sphere is identi- cal to the field of a spinning spherical shell, with the identification ơRa-M. Referring back to Ex. 5.11, I conclude that (6.16) inside the sphere, while the field outside is the same as that of a perfect dipole. 3 Notice that the internal field is uniform, like the electric field inside a uniformly polarized sphere (Eq. 4.14), although the actual formulas for the two cases are curiously different G in place of-3) The external fields are also analogous: pure dipole in both instances.

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