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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, inside the shell, will remain zero even after dumping a billion coulombs of charge on the shell.

Step by step solution

01

Understanding the given problem

The problem states that you're sitting inside an uncharged, hollow spherical shell, and suddenly a charge is dumped on the shell. It is asked to find out the change in the electric field at your location.
02

Apply Gauss's Law

By Gauss's law, the electric field inside a spherical shell is zero at all points. The law states that the total electric flux out of a closed surface is equal to the charge enclosed divided by the permittivity. For any point inside the shell, the enclosed charge is zero. Therefore, the electric field inside the shell is zero, no matter how much charge is on the shell.
03

Conclude the problem

The electric field at the location inside the shell would remain zero even after dumping a billion coulombs of charge on the shell, as the electric field inside a uniformly charged shell is zero.

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Most popular questions from this chapter

You're an engineer for a cable TV company that delivers signals over coaxial cables consisting of an inner wire and a concentric cylindrical outer conductor. A new colleague in your department is worried that electric fields from charge on the outer conductor will interfere with other electrical signals. Formulate an argument to convince your colleague that, as long as the conductors carry equal but opposite charges, any electric field associated with the cable can't extend beyond the outer conductor.

An electron close to a large, flat sheet of charge is repelled from the sheet with a 1.8 -pN force. Find the surface charge density on the sheet.

A long, thin wire carrying \(5.6 \mathrm{nC} / \mathrm{m}\) runs down the center of a long, thin-walled, pipe with radius \(1.0 \mathrm{cm}\) carrying \(-4.2 \mathrm{nC} / \mathrm{m}\) spread uniformly over its surface. Find the electric field (a) \(0.50 \mathrm{cm}\) from the wire and (b) \(1.5 \mathrm{cm}\) from the wire.

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

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