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# HW8 - Physics 3122 Fall 2010 Homework Set 8 Solutions 3.16...

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Physics 3122, Fall 2010: Homework Set 8 Solutions. 3.16 P 3 ( x ) = 1 2 3 3! d dx Λি Νয় Μ৏ Ξ৯ Πਏ Ο৿ 3 ( x 2 1) 3 = 1 48 d 3 dx 3 ( x 6 3 x 4 + 3 x 2 1) = (5 x 3 3 x )/2 (1 x 2 ) d 2 P 3 ( x )/ dx 2 2 xdP 3 ( x )/ dx + 3(3 + 1) P 3 ( x ) = (1 x 2 )15 x 2 x (15 x 2 3)/2 + 12(5 x 3 3 x )/2 = 15 x 15 x 3 15 x 3 + 3 x + 30 x 3 18 x = 0 (or) Q ( θ ) = P 3 (cos θ ) = (5cos 3 θ 3cos θ )/2 sin θ dQ / d θ = ( 15cos 2 θ sin 2 θ + 3sin 2 θ ) (sin θ ) 1 d (sin θ dQ / d θ )/ d θ = (30cos θ sin 2 θ 30cos 3 θ + 6cos θ )/2 = (30cos θ 30cos 3 θ 30cos 3 θ + 6cos θ )/2 = 12(5cos 3 θ 3cos θ )/2 = 12 Q P 3 ( x ) P 1 ( x ) dx 1 1 = 1 2 (5 x 3 3 x ) xdx 1 1 = 1 2 (5 x 4 3 x 2 ) dx 1 1 = 1 2 x 5 x 3 [ ] 1 1 = 0 3.19 V ( in ) ( r , θ ) = A r P (cos θ ) = 0 V ( out ) ( r , θ ) = B r 1 P (cos θ ) = 0 V continuous at r = R A R = B R 1 B = A R 2 + 1 E r ( in ) ( R , θ ) = A R 1 P (cos θ ) = 0 E r (out) ( R , θ ) = B ( + 1) R 2 P (cos θ ) = 0

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HW8 - Physics 3122 Fall 2010 Homework Set 8 Solutions 3.16...

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