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Chapter 21: Problem 38

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
The electric field strength just outside the surface of the conducting sphere is approximately \(1.58 \times 10^{5} \mathrm{N} / \mathrm{C}\).

Step by step solution

01

Understand the Problem

We have to find the electric field strength just outside the conducting sphere carrying surface charge density \(1.4 \mu \mathrm{C} / \mathrm{m}^{2}\). Assume that σ is the surface charge density.
02

Use Gauss's Law

According to Gauss's law, the electric field (E) just outside a conductor is given by the equation \( E = \frac{\sigma}{\varepsilon_{0}} \), where \( \varepsilon_{0} \) is the permittivity of free space. The value of \( \varepsilon_{0} \) is approximately \(8.85 \times 10^{-12} \mathrm{C}^{2} / \mathrm{N} \cdot \mathrm{m}^{2}\).
03

Substitute the Given Value

Substitute the given surface charge density value \( \sigma = 1.4 \mu \mathrm{C} / \mathrm{m}^{2} = 1.4 \times 10^{-6} \mathrm{C} / \mathrm{m}^{2} \) into the equation to find the electric field strength.
04

Calculate Electric Field

Calculate the electric field strength E using the formula derived from Gauss's law: \( E = \frac{\sigma}{\varepsilon_{0}} = \frac{1.4 \times 10^{-6} \mathrm{C} / \mathrm{m}^{2}}{8.85 \times 10^{-12} \mathrm{C}^{2} / \mathrm{N} \cdot \mathrm{m}^{2}}\).

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Most popular questions from this chapter

The electric flux through a closed surface is zero. Must the electric field be zero on that surface? If not, give an example.

A point charge of \(-2 Q\) is at the center of a spherical shell of radius \(R\) carrying charge \(Q\) spread uniformly over its surface. Find the electric field at (a) \(r=\frac{1}{2} R\) and (b) \(r=2 R\). (c) How would your answers change if the charge on the shell were doubled?

Positive charge is spread uniformly over the surface of a spherical balloon \(70 \mathrm{cm}\) in radius, resulting in an electric field of \(26 \mathrm{kN} / \mathrm{C}\) at the balloon's surface. Find the field strength (a) \(50 \mathrm{cm}\) from the balloon's center and (b) \(190 \mathrm{cm}\) from the center. (c) What's the net charge on the balloon?

A solid sphere \(10 \mathrm{cm}\) in radius carries a \(40-\mu \mathrm{C}\) charge distributed uniformly throughout its volume. It's surrounded by a concentric shell \(20 \mathrm{cm}\) in radius, also uniformly charged with \(40 \mu \mathrm{C}\). Find the electric field (a) \(5.0 \mathrm{cm},\) (b) \(15 \mathrm{cm},\) and (c) \(30 \mathrm{cm}\) from the center.

A flat surface with area \(2.0 \mathrm{m}^{2}\) is in a uniform \(850-\mathrm{N} / \mathrm{C}\) electric field. Find the electric flux through the surface when it's (a) at right angles to the field, (b) at \(45^{\circ}\) to the field, and (c) parallel to the field.
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