# How Does a Dielectric Influence Charge Induction on a Conducting Shell?

• Karl86
In summary, the conversation discusses a conducting sphere surrounded by a dielectric and another conducting shell, and the charge induced on the outer shell by the sphere and the dielectric. The equations used are ##D=\epsilon_0E + P## and the Gaussian surface method. The conclusion is that there is no free net charge on the outer shell, but there may be a charge distribution on its inner surface.
Karl86

## Homework Statement

Imagine having a conducting sphere with free charge ##Q## surrounded by a spherical shell filled with a dielectric and then a conducting spherical shell with no free net charge. I want to find out the charge induced on the spherical conducting shell by the sphere or by the dielectric.

## Homework Equations

##D=\epsilon_0E + P##

## The Attempt at a Solution

The dielectric being polarized, at its interface with the conducting spherical shell there will be a charge distribution ##\sigma## attracted by the bounded surface charge ##\sigma_b## of the dielectric and also by the charged sphere. Thus both the electric field ##E## and the electric displacement field ##D## will be discontinuous. Even though there is no free net charge in the spherical shell. Is this reasoning correct?
In other words, my doubt can be restated: is there some free charge at the inner surface of the spherical shell, even though the conducting shell has no net free charge?

You are on the right track. Consider a spherical concentric Gaussian surface entirely inside the conducting shell.
1. What is the electric flux through the surface?
2. What does the answer to the previous question imply about the free charge enclosed by the surface?
3. What do the answers to the previous two questions imply about the free charge on the outer surface of the conducting shell?

## 1. What is induced charge on a conductor?

Induced charge on a conductor refers to the redistribution of electric charges on a conductor due to the presence of an external electric field.

## 2. How is induced charge created on a conductor?

Induced charge is created on a conductor when it is placed in an external electric field, causing the free electrons within the conductor to redistribute and create a net charge on the surface of the conductor.

## 3. What is the difference between induced charge and static charge?

The main difference between induced charge and static charge is that induced charge is temporary and results from the presence of an external electric field, while static charge is a permanent buildup of charge on an object due to the transfer of electrons.

## 4. How does the shape of a conductor affect the distribution of induced charge?

The shape of a conductor can affect the distribution of induced charge, as sharp edges and points can create areas of higher electric field strength, leading to a greater concentration of induced charge.

## 5. Can induced charge be controlled or manipulated?

Yes, induced charge can be controlled or manipulated by changing the external electric field, such as using a grounded object to neutralize the induced charge on a conductor or using a Faraday cage to shield the conductor from electric fields.

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