# Solid Conducting sphere inside a conducting spherical shell

• phymateng
In summary, the problem involves a solid conducting sphere with a negative charge and a concentric conducting spherical shell with a net positive charge. The charge on the inner surface of the shell is Q'2 and the charge on the outer surface is Q''2. Using the fact that the electric field inside a conductor is zero in equilibrium, the charge on the outer shell can be calculated by subtracting the charge on the inner surface from the net charge on the shell. In this case, Q''2 is calculated to be 20.4 pC.
phymateng

## Homework Statement

Consider a solid conducting sphere with a radius 0.7 cm and charge −7.3 pC on it. There is a conducting spherical shell concentric to the sphere. The shell has an inner radius 2.8 cm(with 2.8 cm > 0.7 cm) and outer radius 5 cm and a net charge 27.9 pC on the shell. Denote the charge on the inner surface of the shell by Q′2 and that on the outer surface of the shell by Q′′2. Find the charge Q′′2. Answer in units of pC

## Homework Equations

I got this problem wrong and don't know why.
Shouldn't Q''2 be 0 since the sphere is negative on the surface and attracting the positive charges on the inner shell. The shell should be stable since its a conductor and its Electric field inside is=0. Therefore, the Charge outside the shell is 0.

## The Attempt at a Solution

Conceptually I thought
inside the shell should be the opposite of the charge of the sphere. Since the sphere is negative, then the charge Q'2 inside surface of the shell is same charge but positive. So Q inside shell + Q'2 inside surface of shell = Q''2 outside shell (of whole sphere). For the conducting sphere to be in equilibrium Q''2 should just be 0.

phymateng said:

## Homework Statement

Consider a solid conducting sphere with a radius 0.7 cm and charge −7.3 pC on it. There is a conducting spherical shell concentric to the sphere. The shell has an inner radius 2.8 cm(with 2.8 cm > 0.7 cm) and outer radius 5 cm and a net charge 27.9 pC on the shell. Denote the charge on the inner surface of the shell by Q′2 and that on the outer surface of the shell by Q′′2. Find the charge Q′′2. Answer in units of pC

## Homework Equations

I got this problem wrong and don't know why.
Shouldn't Q''2 be 0 since the sphere is negative on the surface and attracting the positive charges on the inner shell. The shell should be stable since its a conductor and its Electric field inside is=0. Therefore, the Charge outside the shell is 0.

## The Attempt at a Solution

Conceptually I thought
inside the shell should be the opposite of the charge of the sphere. Since the sphere is negative, then the charge Q'2 inside surface of the shell is same charge but positive. So Q inside shell + Q'2 inside surface of shell = Q''2 outside shell (of whole sphere). For the conducting sphere to be in equilibrium Q''2 should just be 0.

The essential point in this problem is that the electric field inside a conducting object is zero when the charges are in equilibrium. Therefore the charge on the outer spherical shell arranges itself so that it cancels the electric field due to the inner solid conducting sphere. That means there will be some charge left over and this charge will flow to the outer surface. Remember free charge on a conductor flows to the outer surface. (Gauss's law is used to prove this.)

Q''2=207.9-7.3=20.4 pC;
Q'2=7.3 pC;

## 1. What is a solid conducting sphere inside a conducting spherical shell?

A solid conducting sphere inside a conducting spherical shell refers to a situation where a solid object made of conductive material (such as metal) is placed inside another larger object also made of conductive material. The two objects have the same center and their surfaces are in contact with each other.

## 2. How does the presence of a solid conducting sphere inside a conducting spherical shell affect the electric field inside the shell?

The presence of a solid conducting sphere inside a conducting spherical shell causes the electric field inside the shell to be zero. This is because the electric field lines inside the shell are affected by the presence of the solid sphere and are redistributed in a way that cancels out the field inside the shell.

## 3. What happens to the charge distribution on the surface of the solid conducting sphere inside a conducting spherical shell?

The charge distribution on the surface of the solid conducting sphere inside a conducting spherical shell becomes non-uniform. This is due to the redistribution of the electric field inside the shell, which causes more charge to accumulate on one side of the sphere than the other.

## 4. What is the significance of the radius of the solid conducting sphere in relation to the radius of the conducting spherical shell?

The ratio of the radius of the solid conducting sphere to the radius of the conducting spherical shell is important in determining the electric field and charge distribution inside the shell. If the ratio is large, the electric field inside the shell will be stronger and the charge distribution on the surface of the sphere will be more non-uniform.

## 5. Can a solid conducting sphere inside a conducting spherical shell exist in an external electric field?

Yes, a solid conducting sphere inside a conducting spherical shell can exist in an external electric field. However, the presence of the external field will affect the electric field and charge distribution inside the shell. The strength of the external field will also affect the ratio of the radii of the two objects.

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