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Chapter 21: Problem 12

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?

Short Answer

Expert verified
The electric field at your location remains zero, regardless of the additional charge to the shell, as stated by Gauss's law. Electric field inside a uniformly charged hollow spherical shell is always zero.

Step by step solution

01

Concept of Electric Field

Electric field is a vector field that shows the distribution of electric forces around charges. It is a basic concept in electromagnetism.
02

Gauss's law

Gauss's law is a basic principle of the electromagnetic theory, it states that the total electric flux through a closed surface is equal to 1/蔚鈧� (where 蔚鈧� is the permittivity of free space) times the charge enclosed by the surface. According to the symmetry of a spherical shell and Gauss's law, the electric field inside a spherical shell with a uniform charge distribution is zero.
03

Apply Gauss's law to the given problem

Despite the fact that a large amount of charge (1 billion coulombs) is distributed uniformly on the shell, this won't affect the electric field at a location inside the shell. The total electric flux through any closed surface wholly contained in the shell must be zero because there's no enclosed charge. This implies the electric field at each point inside the shell is zero.

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Most popular questions from this chapter

If the flux of the gravitational field through a closed surface is zero, what can you conclude about the region interior to the surface?

Under what conditions can the electric flux through a surface be written as \(E A,\) where \(A\) is the surface area?

A long, solid rod \(4.5 \mathrm{cm}\) in radius carries a uniform volume charge density. If the electric field strength at the surface of the rod (not near either end) is \(16 \mathrm{kN} / \mathrm{C},\) what's the volume charge density?

An infinitely long solid cylinder of radius \(R\) carries a nonuniform charge density given by \(\rho=\rho_{0}(r / R),\) where \(\rho_{0}\) is a constant and \(r\) is the distance from the cylinder's axis. Find an expression for the magnitude of the electric field as a function of position \(r\) within the cylinder.

A 2.6 - \(\mu\) C charge is at the center of a cube \(7.5 \mathrm{cm}\) on each side. What's the electric flux through one face of the cube? (Hint: Think about symmetry, and don't do an integral.)
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