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Chapter 21: Problem 40

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

Short Answer

Expert verified
To get the short answer, solve the expression from the final step. After simplification, you will get the magnitude of the electric field strength just outside the surface of the conducting sphere.

Step by step solution

01

Identify given values

From the problem statement, the surface charge density \(\sigma\) is given as \(1.4 \mu C/m^{2}\). This needs to be converted to \(C/m^{2}\). So, \(1.4 \mu C/m^{2} = 1.4 \times 10^{-6} C/m^{2}\). The permittivity of free space \(\varepsilon_0\) is a constant, which equals \(8.85 \times 10^{-12} C^{2}/(N \cdot m^{2})\).
02

Apply the formula for electric field strength

The electric field \(E\) just outside the surface can be determined using the formula \(E = \sigma / \varepsilon_0\). Substituting the values, we get \(E = 1.4 \times 10^{-6} C/m^{2} / 8.85 \times 10^{-12} C^{2}/(N \cdot m^{2})\).
03

Solve for Electric field strength

Calculate the given expression which will provide the value of electric field strength in \(N/C\).

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Most popular questions from this chapter

A spherical shell of radius \(15 \mathrm{cm}\) carries \(4.8 \mu \mathrm{C}\) distributed uniformly over its surface. At the center of the shell is a point charge. If the electric field at the sphere's surface is \(750 \mathrm{kN} / \mathrm{C}\) and points outward, what are (a) the point charge and (b) the field just inside the shell?

Can electric field lines ever cross? Why or why not?

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

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

A solid sphere of radius \(R\) carries a nonuniform volume charge density \(\rho=\rho_{0} e^{r / R},\) where \(\rho_{0}\) is a constant and \(r\) is the distance from the center. Find an expression for the electric field strength at the sphere's surface.
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