Question

(6.) An infinite line of charge is parallel to the plane of an infinite sheet of charge. If the line of charge is a distance b above the sheet, what is the relationship between the densities , o and the distance b that will allow the net field created by the distributions to be zero at some point between the two? Ş+++++++++++++++++++++ + + + + + + + + + + + + + + + + + + + + + + 0

Answer 1

Few problems of electrostatics

- Electric field due to the te infinite line charge of density at a distance r, z 2T ER Hore the electric field acts downwards. Electric field due to the ind infinite sheet of charge having density o at any distance from it face This field acts upwards. For zero net field, 2 TEOR, on 20 Co For the this to happen at some point between linear theag charge and sheet of charge op t co . This is the required relation (s) All charge. in the sphere inside moves to to its suface : Drawing a concentric spherical o Gaussian surface with an r <a., and applying Gausus have, S 4T 22 E 2 9 ( enclosed charge 2o) . Ezo electric field is zero in region giventyr <a

lilj a <p < Drawing a similar to of Gaussian surface but with radius & satisfying a<r<b, we get applying the same lane, 5 X 10 Апт Е2 во n Ę 25x109 ATEO 22 = 9X109 x 5X10-9 2 15 N/C no if & is the momorical - value of radius measured D E 2 in m anche (p is the numerical value 45 N/C of radius measured in m) .!!! . - ) We dramono a similar Gaussian surface a but with radius & satisfying ucrcc.. Enclosed charge a snc - 5mC. bound charge on the inner set surface of the shell 20 - upplying Gauss' lane, AT PE z oo : Ezo : electric field is o in the region b<p <c

Gaussian surface We droame a similar tent with rc Then atire - 4 Tirze = (5x109 - 5x109 20 for nyc., electric field in o.