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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 if it wasn't, the free charges within the conductor would feel a force and hence move, violating our assumption of electrostatic equilibrium.

Step by step solution

01

Understanding the general properties of conductors

In conductors, free electrons can move freely. When the conductor is in electrostatic equilibrium (meaning there are no net forces), these electrons distribute themselves in such a way that they neutralize the external electric field within the conductor, effectively making it zero.
02

Grasping the concept of an electric field inside a conductor

Let's assume that there is an electric field inside the conductor. The drift velocity of the free electrons \(v_d\) (velocity due to the electric field) will be given by \(v_d = \mu E\) where \( \mu \) is the mobility of electron and \( E \) is the electric field. This would cause a current. However, we have assumed that the system is in electrostatic equilibrium, i.e., not changing with time. This contradicts the presence of a current, hence, there cannot be an electric field in a conductor at electrostatic equilibrium.
03

Explaining why the electric field cannot exist inside the conductor at equilibrium

If there was an electric field inside the conductor, then the free charges would experience a force \( F = qE \) (where \( q \) is the charge and \( E \) is the electric field) and therefore move, violating the condition of electrostatic equilibrium. Hence, the electric field on the inside of a conductor in electrostatic equilibrium must be zero to avoid this contradiction.

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Most popular questions from this chapter

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.

A rod \(50 \mathrm{cm}\) long and \(1.0 \mathrm{cm}\) in radius carries a 2.0-\(\mu \mathrm{C}\) charge distributed uniformly over its length. Find the approximate magnitude of the electric field (a) \(4.0 \mathrm{mm}\) from the rod surface, not near either end, and (b) 23 m from the rod.

A point charge \(-q\) is at the center of a spherical shell carrying charge \(+2 q .\) That shell, in turn, is concentric with a larger shell carrying \(-\frac{3}{2} q .\) Draw a cross section of this structure, and sketch the electric field lines using the convention that eight lines correspond to a charge of magnitude \(q.\)

A solid sphere \(25 \mathrm{cm}\) in radius carries \(14 \mu \mathrm{C},\) distributed uniformly throughout its volume. Find the electric field strength (a) \(15 \mathrm{cm},\) (b) \(25 \mathrm{cm},\) and (c) \(50 \mathrm{cm}\) from its center.

Why can't you use Gauss's law to determine the field of a uniformly charged cube? Why couldn't you use a cubical Gaussian surface?
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