Question

a) Performing an integral over point-charges (Coulomb's Law) to determine electric field. A cylinder of length Land uniform density p is centered at the origin, with its axis pointing along the 2-direction. Determine the electric field at point X which is a distance a>L/2 from the origin along the z-axis. Please set up the integral carefully-you do not need to evaluate it. z axis b) Which components of the electric field do you expect to be zero? Explain. c) How should the electric field depend on distance from the cylinder, when very far away from the cylinder? Explain.

Answer 1

& obtaining Expression for Electric field Coordinate + 2 let us candidate the Cylindrical, s/m. i-e (8, 8, 2) Cordinates. 227 7 , 21) source print (SP) 2 a do £10,42) Zac 1916, plane, OI xy phone to field point (FP) fecimi Sp: 194,2) F-P: (5,4,0) R = \f-p-5P) R = ipê -zá) IRI= √872² letle be the uniform charge density Here I = 9-(as given 1. in question) R få mit vector alus we know that, do= gede dq=pdz we know that, de = Sedz ar Unto (F/? de = (dz (sås -zar) 42 to Vp722 Vp + ? z Cancel out Aca de 2

In the fig. Shows above for every do (tz) there exist another day at (-2) dircen sie in opposite dirce". This indood indicates the charge configuration is symmetric about Zzo plane (XY plane). Hence in the resultant field, there is a cancellation of '² components. Therefore the field intensity will be along the radial diree". ter to the line Z=o). de = Se (gar - zaz) unho (87 2²}} E = Pe Isaz cap) unto I (pt2²% 23-ye let z= stano dz= pseere do Unit of a (-2/ to ap) E = Pe 11 s. gseco do cap) = le pt sech (ay) 13 +p+ +69283/2 VEGA , 1927{1+taupe) 32 - Untol s secson ziren les de la 4hEog hl ปวital) KEP (leuit weeter 1.7cxls) Eine & 1 6 Erine a l Lerdistance a Pene (E=f. "Ale to the question are a and Ler distance s a