Question

Two Charges q>0 are located at r1=(d/2, 0,d/2) and r2=(-d/2,0,d/2) above an infinite conducting plate in the xy plane at z=0. The plate is grounded. Determine the induced charge density on the plate at z=0. Sketch this charge distribution along the line y = 0 and along the line x = 0. On your sketches indicate its sign and approximate magnitude as a function of x and y respectively. Interpret your results.

Answer 1

Graph.1

Graph2.

Note: Above graphs show the order of the magnitude of charge density, not its actual value.

fint we have to find the electric field of the system, which we will calculate using methods of image 8. +2.2 i 1. +? God) (2008) -.;- ya -2 (40)! (,0-5) image charges are represented by and 2'. Now using E= q gt 47160 T713 we get EC2,9.7) = -) +GVJI+LE-ZÉ 4760 LC (1-2); 42+(-73039% Hl-x) + (-4)3+ (4.23€ (-*_x) 346-VJIH -ZJR tel +x)4++(4-2)^J" Tid 1x127 42 t/d 117 - (L-x) + (-4)3 + F¢-z)736 [(-x)²+4²+ ( 2 / + )² valid for ZZ, 1-0) -

to find o we use the boundary condition El abovelo - Ebelow laco - 2 here Ezo for all values of zo. and so odpovednosta - oz GoEabarelys -611) aboye '?=0 from ean el Endove la Tee-x)** + (yey! Tw2Y4A 9**** pport ** t DÊ [(483*** *6poplu 557 97" [(4-2) ?7v (gegee putting this value of t in eqh (W) We get desired result for o.