Answered: m', and 03 for the electric field to be…

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.

m', and 03
for the electric field to be
%3D
1 2 3
Figure 7
ing spherical shell of inner
olid sphere and has a net

Expert Solution

Step 1

let E₁,E₂and 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 / 2ϵ_o ------(2)

where σ = surface charge density

ϵ_o= permitivitty of free space = 8.854 x 10^-12 F/m

substituting (2) in (1) we get

σ ₃ / 2ϵ_o= σ ₁ / 2ϵ_o+ σ₂ / 2ϵ_o

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