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Chapter 21: Problem 33

Find the field produced by a uniformly charged sheet carrying \(87 \mathrm{pC} / \mathrm{m}^{2}\).

Short Answer

Expert verified
The electric field produced by the uniformly charged sheet is \(4.92 \mathrm{N/C}\).

Step by step solution

01

Convert charge to standard units

We need to convert the surface charge density from pC/m\(^2\) to C/m\(^2\). Given \(87 \mathrm{pC}/\mathrm{m}^{2}\), the conversion from pC (picocoulombs) to C (coulombs) is 1C = 1e12 pC. Hence, \(\sigma = 87 \times 10^{-12} \mathrm{C}/\mathrm{m}^{2}\).
02

Substitute values into formula

Substitute the values of \(\sigma\) and \(\epsilon_0\) into the formula \(E = \sigma / 2\epsilon_0\). The permittivity of free space, \(\epsilon_0\), is approximately \(8.85 \times 10^{-12} \mathrm{C}^{2}/\mathrm{N}\cdot\mathrm{m}^{2}\).
03

Calculate the electric field

Calculate the electric field by plugging in the values into the formula. The result is \(E = (87 \times 10^{-12}) / (2 \times 8.85 \times 10^{-12}) = 4.92 \mathrm{N/C}\). The field points away from the sheet if the charge is positive, and toward the sheet if the charge is negative.

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Most popular questions from this chapter

What's the approximate field strength \(1 \mathrm{cm}\) above a sheet of paper carrying uniform surface charge density \(\sigma=45 \mathrm{nC} / \mathrm{m}^{2} ?\)

Eight field lines emerge from a closed surface surrounding an isolated point charge. Would the number of field lines change if a second identical charge were brought to a point just outside the surface? If not, would anything change? Explain.

You're sitting inside an uncharged, hollow spherical shell. Suddenly someone dumps a billion coulombs of charge on the shell, distributed uniformly. What happens to the electric field at your location?

A study shows that mammalian red blood cells (RBCs) carry electric charge resulting from 4.4 million (rabbit cells) to 15 million (human cells) excess electrons spread over their surfaces. Approximating rabbit and human RBCs as spheres with radii \(30 \mu \mathrm{m}\) and \(36 \mu \mathrm{m},\) respectively, find the electric field strengths at the cells' surfaces.

What is the electric field strength just outside the surface of a conducting sphere carrying surface charge density \(1.4 \mu \mathrm{C} / \mathrm{m}^{2} ?\)
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