# HW05sol - Classical Electrodynamics I PHY 505 Fall 2010 Homework 5 with solutions Problem 5.1(to be graded of 10 points Use the method of images to

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1 C:\User\Teaching\505-506\F10\HW05sol.doc PHY 505 Classical Electrodynamics I Fall 2010 Homework 5 with solutions Problem 5.1 (to be graded of 10 points). Use the method of images to find the Green’s function of the system shown in Fig. on the right. (The bulge on the conducting plane has the shape of a semi-sphere of radius R .) Solution : Let a (real) point charge q 1 be at point r 1 , with r 1 R . Then all the boundary conditions may be satisfied using three charge images (see Fig.), with , , , , , , , 3 2 3 4 1 1 2 4 1 3 1 3 1 3 1 2 1 2 1 1 2 r r ρ ρ r r r R r R q q q z z q q r R r R q q where j is the horizontal component of radius-vector r j , and z j is its vertical component. As a result, the Green’s function may be presented simply as . , 1 ) , ( 1 4 1 1 ' q q G j j j r r r r r' r However, even in the most suitable, cylindrical coordinates, this compact expression becomes rather bulky, because each denominator looks like      2 / 1 2 2 2 cos 2 j j j j j z z  r r , while   . 2 / 1 2 1 2 1 1 z r Problem 5.2 (15 points). Find the 2D Green’s function in: (i) unlimited free space, and (ii) free space above a conducting plane. Use the latter result to calculate the distribution of the electric potential created by the 2D system shown

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## This note was uploaded on 09/10/2011 for the course PHY 505 taught by Professor Stephens,p during the Fall '08 term at SUNY Stony Brook.

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HW05sol - Classical Electrodynamics I PHY 505 Fall 2010 Homework 5 with solutions Problem 5.1(to be graded of 10 points Use the method of images to

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