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Chapter 22: Problem 11

Is the potential at the center of a hollow, uniformly charged spherical shell higher than, lower than, or the same as at the surface?

Short Answer

Expert verified
The electric potential at the center of a hollow, uniformly charged spherical shell is the same as at the surface.

Step by step solution

01

Understanding the Basics

We need to know first that the electric field inside a hollow, uniformly charged sphere is zero. This is a consequence of Gauss's Law. Which states that the net electric flux through a closed surface is equal to the charge enclosed by the surface divided by the permittivity of the medium.
02

Applying Gaussian Surface Concept

If we consider a Gaussian surface inside the shell, the charge enclosed by this surface is zero. Hence, by Gauss's Law, the electric field is zero everywhere inside the shell.
03

Calculating Electric Potential

The electric potential V for a location in an electric field is calculated by the negative of the work done by an external agent in moving a unit positive charge from an arbitrary reference point to that point, without any acceleration. Now, as there is no electric field inside the sphere, we can move a unit positive charge from the surface (let's call it point A) to the center (point B) with no work done. Hence the electric potential difference between the surface and the center \(\Delta V=V_B-V_A=0\).

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Most popular questions from this chapter

What's the potential difference between the terminals of a battery that can impart \(7.2 \times 10^{-19} \mathrm{J}\) to each electron that moves between the terminals?

The electric field within a cell membrane is approximately \(8.0 \mathrm{MV} / \mathrm{m}\) and is essentially uniform. If the membrane is \(10 \mathrm{nm}\) thick, what's the potential difference across the membrane?

A conducting sphere \(5.0 \mathrm{cm}\) in radius carries \(60 \mathrm{nC} .\) It's surrounded by a concentric spherical conducting shell of radius \(15 \mathrm{cm}\) carrying \(-60 \mathrm{nC}\). (a) Find the potential at the sphere's surface, taking \(V=0\) at infinity. (b) Repeat for the case when the shell carries \(+60 \mathrm{nC}\)

Three equal charges \(q\) form an equilateral triangle of side \(a\). Find the potential at the center of the triangle.

The potential difference between the surface of a 3.0 -cm-diameter power line and a point \(1.0 \mathrm{m}\) distant is \(3.9 \mathrm{kV}\). Find the line charge density on the power line.
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