Physics for Scientists and Engineers: Foundations and Connections
1st Edition
ISBN:9781133939146
Author:Katz, Debora M.
Publisher:Katz, Debora M.
Chapter25: Gauss’s Law
Section: Chapter Questions
Problem 45PQ: What is the magnitude of the electric field just above the middle of a large, flat, horizontal sheet...
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Question
Three large charged insulating sheets have charge per unit area of σ1 = +1µC/m2, σ2 = −2µC/m2, and σ3, as shown in Figure 7. What is the charge density of sheet 3, σ3, in order for the electric field to be
zero in the region between sheets 2 and 3.
Expert Solution
Step 1
let E1,E2 and E3 be the respective electric fields due to the sheets 1,2 and 3.
In the region between 2 and 3 for the electric field to be zero,
=> E3 = E1 + E2 ------(1)
Electric field due to a charged sheet is given by E = σ / 2ϵo ------(2)
where σ = surface charge density
ϵo = permitivitty of free space = 8.854 x 10-12 F/m
substituting (2) in (1) we get
σ 3 / 2ϵo = σ 1 / 2ϵo + σ2 / 2ϵo
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