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# ch24_p58 - 58 Since the charge distribution is spherically...

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58. Since the charge distribution is spherically symmetric we may write E r q r b g = 1 4 π 0 ε encl , where q encl is the charge enclosed in a sphere of radius r centered at the origin. (a) For r = 4.00 m, R 2 = 1.00 m and R 1 = 0.500 m, with r > R 2 > R 1 we have (in SI units) ( ) 9 6 6 3 1 2 2 2 (8.99 10 )(2.00 10 1.00 10 ) 1.69 10 V/m. 4 (4.00) q q E r r ε + × × + × = = = × 0 π (b) For R 2 > r = 0.700 m > R 2 ( ) 9 6 4 1 2 2 (8.99 10 )(2.00 10 ) 3.67 10 V/m. 4 (0.700) q E r r ε × × = = = × 0 π (c) For R 2 > R 1 > r , the enclosed charge is zero. Thus, E = 0. The electric potential may be obtained using Eq. 24-18: V r V r E r dr r r b g b g b g ′ = z . (d) For r = 4.00 m > R 2 > R 1 , we have ( ) 9 6 6 3 1 2 (8.99 10 )(2.00 10 1.00 10 ) 6.74 10 V. 4 (4.00) q q V r r ε + × × + × = = = × 0 π (e) For r = 1.00 m = R 2 > R 1 , we have ( ) 9 6 6 4 1 2 (8.99 10 )(2.00 10 1.00 10 ) 2.70 10 V. 4 (1.00) q q V r r ε + × × + × = = = × 0 π (f) For R 2 > r = 0.700 m > R 2 , ( ) 6 6 9 4 1 2 2 1 2.00 10 1.00 10

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ch24_p58 - 58 Since the charge distribution is spherically...

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