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chap6f hayt - 6.13. Perfectly-conducting concentric spheres...

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Unformatted text preview: 6.13. Perfectly-conducting concentric spheres have radii of 2 and 6 cm. The region 2 < r < 3 cm is filled with a solid conducting material for which = 100 S/m, while the portion for which 3 < r < 6 cm has = 25 S/m. The inner sphere is held at 1 V while the outer is at V = 0. a. Find E and J everywhere: From symmetry, E and J will be radially-directed, and we note the fact that the current, I , must be constant at any cross-section; i.e., through any spherical surface at radius r between the spheres. Thus we require that in both regions, J = I 4 r 2 a r The fields will thus be E 1 = I 4 1 r 2 a r (2 < r < 3) and E 2 = I 4 2 r 2 a r (3 < r < 6) where 1 = 100 S/m and 2 = 25 S/m. Since we know the voltage between spheres (1V), we can find the value of I through: 1V = Z . 03 . 06 I 4 2 r 2 dr Z . 02 . 03 I 4 1 r 2 dr = I . 24 1 1 + 1 2 and so I = . 24 (1 / 1 + 1 / 2 ) = 15 . 08A Then finally, with I = 15 . 08 A substituted into the field expressions above, we find...
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This note was uploaded on 10/02/2011 for the course EE 1 taught by Professor Joshi during the Fall '08 term at UCLA.

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chap6f hayt - 6.13. Perfectly-conducting concentric spheres...

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