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Chapter 21: Problem 32

An electron close to a large, flat sheet of charge is repelled from the sheet with a 1.8 -pN force. Find the surface charge density on the sheet.

Short Answer

Expert verified
The surface charge density \(σ\) on the large flat sheet approximates \(19.8 nC/m^2\).

Step by step solution

01

Identify Given & Needed Variables

We have the force \(F = 1.8 \, pN = 1.8 \times 10^{-12} N\), and we know that the charge \(q = -1.6 \times 10^{-19} C\). We want to find the surface charge density \(σ\).
02

Arrange the Equation

We want to derive \(σ\) from the equation \(F = σq/2ε_0\). First, let's arrange the equation into \(σ = 2FE_0/q\). In this equation, \(ε_0\) is the permittivity of free space, and its value is approximately \(8.85 x 10^{-12} C^2/N•m^2\).
03

Solve the Equation

Substitute the given values into the rearranged equation: \(σ = 2*(1.8*10^{-12}N)*(8.85x10^{-12}C^2/N•m^2)/(1.6x10^{-19}C)\). Calculate the result to find \(σ\).

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