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Chapter 21: Problem 15

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

Short Answer

Expert verified
The electric field must be zero inside a conductor in electrostatic equilibrium because electrostatic equilibrium implies that the charges inside the conductor are not moving. In a conductor, charges are free and will move to cancel out any internal electric field. The fact that they're not moving (because of electrostatic equilibrium) proves that they have succeeded in cancelling out the internal electric field, making it zero.

Step by step solution

01

Understanding Electrostatic Equilibrium

Electrostatic equilibrium is a state where the electric charges within a system do not move. This is caused by the lack of an electric field that would cause the charges to push or pull on each other. Since there's no net force, there's no acceleration, so charges are in equilibrium.
02

Properties of a Conductor

In a conductor, the charges are free to move. In situations where there is an external electric field applied to the conductor, the charges move in a way that cancels out this external electric field inside the conductor. They distribute themselves on the surface of the conductor.
03

Zero Electric field Inside a Conductor

In electrostatic equilibrium, these free charges have already moved to their equilibrium positions, such that the electric field everywhere inside the conductor is zero. If there were a non-zero electric field in the conductor, the charges would continue moving. But since they're in electrostatic equilibrium, they don't. From this, we can conclude that the electric field inside a conductor in electrostatic equilibrium must be zero. This property is crucial for many technology applications, such as the shielding effect in coaxial cables and Faraday cages.

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Most popular questions from this chapter

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.

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.

The electric field strength outside a charge distribution and \(18 \mathrm{cm}\) from its center has magnitude \(55 \mathrm{kN} / \mathrm{C}\). At \(23 \mathrm{cm}\) the field strength is \(43 \mathrm{kN} / \mathrm{C} .\) Does the distribution have spherical or line symmetry?

A flat surface with area \(0.14 \mathrm{m}^{2}\) lies in the \(x-y\) plane, in a uniform electric field \(\vec{E}=5.1 \hat{\imath}+2.1 \hat{\jmath}+3.5 \hat{k} \mathrm{kN} / \mathrm{C} .\) Find the flux through the surface.

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.
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