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hw3_p5406_s05

# hw3_p5406_s05 - HW 3 Phys5406 S05 due 1)Use the solution...

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HW 3 Phys5406 S05 due 2/10/05 1)Use the solution found in class for the potential, Φ( r ), inside a conducting box of sides (a,b,c) in the (x,y,z) directions when all sides are grounded except for the side at z = c that is maintained at potential V(x,y). In this problem we will take V(x,y) = V, constant, so that no integral remains in the expression for Φ( r ) . Find the potential at any point inside the box and show that the total charge on the inside surfaces of the box add to zero. 2)We will use the solution for the empty box with V(x,y) = V at z=c to get the Green’s function G D for all problems with this geometry. a) To see the connection between 0 2 G D ( r , r 0 ) = - 4 πδ ( r - r 0 ) and a sine series, expand a one dimensional delta function in the range (0,a) as below, δ ( x - x 0 ) = X j [ A j sin jπx/a sin jπx 0 /a ] , (1) and ﬁnd the coeﬃcients A j . This is called the completeness relation for the sine series, indicating any function f(x), x in the range (0,a), can be expressed as,

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hw3_p5406_s05 - HW 3 Phys5406 S05 due 1)Use the solution...

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