(a) Prove that the average magnetic field, over a sphere of radius R, due to steady currents...
Question:
(a) Prove that the average magnetic field, over a sphere of radius R, due to steady currents within the sphere, is where m is the total dipole moment of the sphere. Contrast the electrostatic result, Eq. 3.105.
[This is tough, so I'll give you a start: Write B as (V x A), and apply Prob. 1.60b. Now put in Eq. 5.63, and do the surface integral first, showing that (see Fig. 5.65). Use Eq. 5.91, if you like.]
(b) Show that the average magnetic field due to steady currents outside the sphere is the same as the field they produce at the center.
Bave Bave M40 2m 47 R3 I ¡fBdr. R³ 1 1/2 d da = 413 4 лг
Step by Step Answer:
34KR Bdr 3 a Bave A x da 473 R J x f da 3 4T R 340 source point r not ...View the full answer
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