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TST3-351-F02

TST3-351-F02 - Dr Gangopadhyaya Test III Physics 351...

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Dr. Gangopadhyaya Test III Physics 351 December 4, 2002 As always, to receive full credit you must show your work in a neat, organized and a legible form. Some Relevant Formuae are given below: V sph ( r, θ, φ ) = X l =0 A l r l + B l r l +1 P l (cos θ ) V cyl ( ρ, φ ) = ( a 0 + b 0 log ρ ) ( c 0 + d 0 φ ) + X n =1 ( a n ρ n + b n ρ - n ) ( c n cos( ) + d n sin( )) ( E 2 - E 1 ) · ˆ n 1 2 = σ ² 0 ; ( E 2 - E 1 ) × ˆ n 1 2 = 0 ; cos( a + b ) = cos a cos b - sin a sin b , P 0 ( x ) = 1 , P 1 ( x ) = x , P 2 ( x ) = 1 2 (3 x 2 - 1) , P 3 ( x ) = 1 2 (5 x 3 - 3 x ) ; Z 1 - 1 dx P m ( x ) P n ( x ) = 2 2 m + 1 δ mn (1 + x ) ν = 1 + νx + ν ( ν - 1) 2! x 2 + ν ( ν - 1)( ν - 2) 3! x 3 + ν ( ν - 1)( ν - 2)( ν - 3) 4! x 4 + · · · ; converges for | x | < 1 . ln (1 + x ) = x - 1 2 x 2 + 1 3 x 3 + · · · + ( - 1) n +1 1 n x n + · · · 1

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1. A spherical shell of radius R and made of an insulating material has a surface charge density σ = σ 0 cos θ sin 2 θ glued on it. a) Express this surface charge density as a linear sum of Legendre polynomials in cos θ . b) Determine the electric potential inside and out side the sphere.
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TST3-351-F02 - Dr Gangopadhyaya Test III Physics 351...

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