Question

7. An infinite conducting plane exists at 2 = 0. At a height of 1 m above the plane is a 2 m line of charge with uniform charge density pl. The line is parallel to the r axis and centered about the z axis (i.e., its endpoints run from (-1,0.1) to (1,0,1)). Provide the expression that can be used to obtain the voltage V(x, y, z) in the space above the plane. You can leave your answer in the form of an integral (or two). The goal is to set up the integrals with as much detail as possible without actually evaluating them.

Answer 1

- An infinite conducting Plane exists at 220 . At a height of in above the ground 220 Plane a dom line of charge AB with uniform charge densiar exists Pex,72) B (~1,0,1) all at on (21,0,1) yz , LA B X ds cal,0,-1) (-1,0,1) 2 Fig. As the infinite conducting Plane existing 2=0 working ground image Charge Lime AB created below 250 plame as shown we have to determine v af Point (x, y,2) im SPQCC we know · VEJEN - so we have to first determine è due to AB and similarly we can get eo due to A'B' lets determine due to any orbitary charge >

Az 2.2) Is de 2002) XL Pernia) (0,0,2) de ✓ figa lets comsider a line charge AB with uniform Charge density sa elm we have to evaluate field intensity P (X,Y,Z). E sman length de im AB dd = fa de Pizda alldz df = dy ar a unora che = (7@+y@yúzáz) -- (7'42) =xantyây + (2-2)2 = das+(2-21 år Pa saht (2=2') a R? TRP 1 Jp2+(2-21)2} }

dE=PL fåst (2-2-) âz e unto Tot (2-2) ? 2/2 Again Parcosk Rafseca 2'=2-Stand [84(2-2) dź= Psecaxdx L = pat polanda apa secak utto the 1 { pas altame8,3 e sedelda often I ara tamkâz de pas de fandâr} I (apse ex) da Psecak I lamaz fan UREO 2 T seca The jo pay case + simma's) do xil I sececosa saa wa Col V rás cose tâu sima) dice CH PL the hos [-(simas - simac) ás+(coses, cor) Now for fig we can get Ei at PC x 14,2) due to AB

Erste r T-(som kg sme) ans +(cosg-cosx, Maz] Utfol - AP and BP with Hence &, and do angles made by the normal from p to P-s normal distance P to AB E = .PL [sinds'- sima,) ap+(cosa ~C054) az] UKEol L Hence ai and dă are angles made by AP and B'p with normal form Pro A BI p!-> Normal distance P to A'B' c Vai P is , Vi :-E702 Sen. liente [-(simog-sim 0,7 ás: [convergaros ja simdo-sima) 2 + (costs costlâzjak 48 to SL - JUNE - (simdasina,lât(cosao-cosa,lao] (a satdzaz) (simdo-sindi) +(coscorcosai lâz7 a cds 9 tdzâz) y PL UTES