# Does Gauss's Law Hold for a Charge Inside a Hollow Conductor?

• ice109
In summary, the conversation discusses the behavior of electric charges inside a hollow conductor. The participants question whether the proximity of a charge to the interior wall of the conductor affects the electric field on the surface. One participant suggests that there may be a buildup of negative charge on the interior wall, which could attract positive charge and create a stronger electric field. However, the other participant argues that according to Gauss's law, the electric field on the outside of the conductor should be zero regardless of the interior charge's position. The conversation ends with a discussion of an exaggerated example and the effect it would have on the electric field.
ice109
i don't understand this. if i have a charge inside a hollow conductor of say +Q and a charge of -Q on the conductor it doesn't matter how close the interior charge is to the wall of the conductor ( but not touching ) the field at all points on the surface of the conductor will be zero? doesn't make sense to me. I'm imagining that if i put the +Q charge close to the interior wall of the conductor there will be a build up of negative charge next to it on the interior wall inside the conductor. This will in effect draw positive charge to that clump of negative charge on the exterior wall of the inside of the conductor and cause a stronger e field there? But ofcourse gauss's law says that the e field will be zero every where on the outside?

Let's use an exaggerated example. Presuming that a stronger negative e- field is forced on the interior wall like you said. If you drew a gaussian sphere around the hollow sphere, which way would this particular electric field point? If you think about it, if a negative charge were to be forced at that particular point, then directly opposite it across the sphere there would be an induced positive charge (since electrons don't come from just anywhere). Would that e field point into or out of the gaussian sphere? Compare these two fields and see the effect.

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## What is Gauss's Law?

Gauss's Law is a fundamental law in electromagnetism that relates the electric field at a point to the electric charge contained within a closed surface surrounding that point.

## What is an electric field?

An electric field is a vector field that describes the strength and direction of the electric force that a charged particle would experience at any point in space.

## How is Gauss's Law used to calculate the electric field?

Gauss's Law can be used to calculate the electric field by calculating the electric flux through a closed surface surrounding the point of interest and dividing it by the total charge enclosed within that surface.

## Can Gauss's Law be applied to any shape or surface?

Yes, Gauss's Law can be applied to any closed surface, regardless of its shape or size, as long as it completely encloses the point of interest and the electric field is uniform across the surface.

## What are some real-life applications of Gauss's Law and electric fields?

Gauss's Law and electric fields have many practical applications, such as in the design of electronic devices, power transmission systems, and medical equipment like MRI machines. They are also used in understanding the behavior of lightning and the Earth's magnetic field.

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