Theory of Images or Gauss's Law for Concentric Conducting Spheres?

In summary, the problem involves two concentric conducting spheres, one grounded and one with a potential of V0, and finding the charge on each sphere when the grounded one is either the outer or inner sphere. The solution involves using image charges from one sphere to the other. The person asking the question initially considered using the theory of images, but has decided that it may be easier to use Gauss's Law. They are curious about the specific image system used.
  • #1
atomicpedals
209
7

Homework Statement



Two conducting spheres are concentric, the radius of the inner being a and the outer being b. One sphere is grounded & the other is at a potential V0. Find the charge on each when the grounded sphere is a) the outer, b) the inner.

2. The attempt at a solution

Is this an appropriate application for theory of images? Or is it a far more straightforward application of Gauss's Law?

I'm tempted to use image charges from one sphere to the other, but fear that's making life harder than it needs to be.
 
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  • #2
Ok, I've become comfortably certain that images are the way to go.
 
  • #3
Out of curiosity, what is your image system?
 

FAQ: Theory of Images or Gauss's Law for Concentric Conducting Spheres?

What is the Theory of Images?

The Theory of Images, also known as Gauss's Law, is a concept in electrostatics that explains how to calculate the electric field and potential due to a charge distribution in the presence of conductors. It is based on the principle that a charged object placed near a conductor will induce an opposite charge distribution on the surface of the conductor.

How is Gauss's Law used in physics?

Gauss's Law is used to calculate the electric field and potential of a charge distribution in the presence of conductors. It is an important tool in understanding the behavior of electric charges and is often used in the design and analysis of electrical systems.

What is the significance of Gauss's Law?

Gauss's Law is significant because it provides a simple and elegant way to calculate electric fields and potentials in situations that would otherwise be mathematically complex. It also helps to explain phenomena such as lightning and the behavior of charged particles in electric fields.

How do I apply Gauss's Law in practical situations?

In practical situations, Gauss's Law is applied by first identifying the charge distribution and any conductors present. Then, the appropriate Gaussian surface is chosen and the electric field and potential are calculated using the integral form of Gauss's Law. Finally, these values can be used to analyze and predict the behavior of the system.

What are some real-world examples of Gauss's Law?

Some real-world examples of Gauss's Law include lightning strikes, the behavior of charged particles in electric fields, and the design of electrical systems such as capacitors and transmission lines. It is also used in the study of atmospheric electricity and the behavior of plasmas in space.

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