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Unformatted text preview: Dr. Gangopadhyaya Final Exam Physics 351 April 25, 2008 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,, ) = X l =0 A l r l + B l r l +1 P l (cos ) (1) V cyl ( , ) = ( a + b log )( c + d ) + X n =1 ( a n n + b n  n ) ( c n cos( n ) + d n sin( n )) (2) ( E 2 E 1 ) n 1 2 = ; ( E 2 E 1 ) n 1 2 = 0 ; cos( a + b ) = cos a cos b sin a sin b (3) P ( 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 ) ; (4) Z 1 1 dx P m ( x ) P n ( x ) = 2 2 m + 1 mn (1 + x ) n = 1 + nx + n ( n 1) 2! x 2 + n ( n 1)( n 2) 3! x 3 + (5) (1 x ) n = 1 + nx + n ( n + 1) 2! x 2 + n ( n + 1)( n + 2) 3! x 3 + (6) ~ dl Cart = dx i + dy j + dz k ~ dl Sph = dr r + r d + r sin d ~ dl Cyl = d + d + dz k (7) Constants: = 1 4 (9 10 9 ) C 2 Nm 2...
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This note was uploaded on 01/28/2010 for the course PHYS 351 taught by Professor Gangopashyaya during the Spring '09 term at Loyola Chicago.
 Spring '09
 Gangopashyaya
 Magnetism, Work

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