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Chapter 21: Problem 38

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

Short Answer

Expert verified
The approximate field strength 1 cm above the sheet of paper carrying uniform surface charge density is \(2.54 x 10^6 N/C\).

Step by step solution

01

Identify given quantities

The surface charge density, \(\sigma\), is given as 45 nC/m^2. This needs to be converted into C/m^2 for consistency in the units, thus \(\sigma = 45 x 10^{-9} C/m^2\). The distance above the sheet of paper is not relevant for calculating the electric field strength, as it does not depend on the distance from the sheet in the near field approximation.
02

Substitute into the formula

Using the formula for the electric field due to a sheet with uniform surface charge density, \(E = \frac{\sigma}{2\epsilon_0}\), substitute the given surface charge density and the permittivity of free space constant into the formula. Thus, \(E = \frac{45 x 10^{-9}}{2 x 8.85 x 10^{-12}}\)
03

Solve

Solving this equation gives \(E \approx 2.54 x 10^6 N/C\).

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Most popular questions from this chapter

Why must the electric field be zero inside a conductor in electrostatic equilibrium?

A nonconducting square plate \(75 \mathrm{cm}\) on a side carries a uniform surface charge density. The electric field strength \(1 \mathrm{cm}\) from the plate, not near an edge, is \(45 \mathrm{kN} / \mathrm{C}\). What's the approximate field strength \(15 \mathrm{m}\) from the plate?

A 250-nC point charge is placed at the center of an uncharged spherical conducting shell \(20 \mathrm{cm}\) in radius. Find (a) the surface charge density on the outer surface of the shell and (b) the electric field strength at the shell's outer surface.

A study shows that mammalian red blood cells (RBCs) carry electric charge resulting from 4.4 million (for rabbit cells) to 15 million (for 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.

A rod \(50 \mathrm{cm}\) long and \(1.0 \mathrm{cm}\) in radius carries a 2.0-\(\mu \mathrm{C}\) charge distributed uniformly over its length. Find the approximate magnitude of the electric field (a) \(4.0 \mathrm{mm}\) from the rod surface, not near either end, and (b) 23 m from the rod.
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