# Finding E fields and potential given a hollow spherical conductor

• SeanLikesRice
In summary, the problem involves calculating the electric field at a distance of 8.0 cm from the center of a hollow spherical conductor with a net charge of 21.5 μC and a radius of 7.8 cm. A point charge of -12.2 μC is located at the center of the hollow. The equation used to solve this problem is E = \frac{kQ}{r^2}, and it is necessary to consider the distribution of charge on the conductor. Gauss' Law may also be applied to determine the electric field in this scenario.
SeanLikesRice
Hello, this is my first post here, so hopefully I do this in the right way...

## Homework Statement

A hollow spherical conductor carries a net charge of 21.5 μC. The radius of the inner hollow is 5.2 cm and thee full radius of the sphere is 7.8 cm. At the center of the sphere, in the middle of the hollow, is a point charge of -12.2 μC.

Find the E field at a distance of 8.0 cm from the center of the sphere.

## Homework Equations

$E = \frac{kQ}{r^2}$

## The Attempt at a Solution

Now when I draw this up in my notebook, I'm a little confused. Since the conductor has a net charge of 21.5 μC, does the point charge of -12.2 μC not matter in terms of finding the E field?

Using the net charge...

$E = \frac{k * 21.5μC}{(8.0cm)^2}$

Is this correct, or d I have to account for the point charge in the center of the hollow sphere?

Think about the distribution of charge on the conductor. What will the charge be on the inside surface?

SeanLikesRice said:
Hello, this is my first post here, so hopefully I do this in the right way...

## Homework Statement

A hollow spherical conductor carries a net charge of 21.5 μC. The radius of the inner hollow is 5.2 cm and thee full radius of the sphere is 7.8 cm. At the center of the sphere, in the middle of the hollow, is a point charge of -12.2 μC.

Find the E field at a distance of 8.0 cm from the center of the sphere.

## Homework Equations

$E = \frac{kQ}{r^2}$

## The Attempt at a Solution

Now when I draw this up in my notebook, I'm a little confused. Since the conductor has a net charge of 21.5 μC, does the point charge of -12.2 μC not matter in terms of finding the E field?

Using the net charge...

$E = \frac{k * 21.5μC}{(8.0cm)^2}$

Is this correct, or d I have to account for the point charge in the center of the hollow sphere?

What does Gauss say? Does he say it matters how the charge inside his surface is distributed?

## 1. How do you calculate the electric field inside a hollow spherical conductor?

The electric field inside a hollow spherical conductor is always zero. This is due to the fact that the charges inside the conductor will redistribute themselves in such a way that the electric field cancels out, resulting in a net electric field of zero.

## 2. What is the formula for calculating the electric field at a point outside a hollow spherical conductor?

The formula for calculating the electric field at a point outside a hollow spherical conductor is E = k * Q / r2, where k is the Coulomb's constant, Q is the total charge on the conductor, and r is the distance from the center of the conductor to the point where the electric field is being calculated.

## 3. How do you find the potential at a point inside a hollow spherical conductor?

The potential at any point inside a hollow spherical conductor is constant and equal to the potential at the surface of the conductor. This is because the electric field inside a conductor is zero, and the potential is directly related to the electric field by the equation V = -∫E * dr. Therefore, the potential inside a hollow spherical conductor is calculated by taking the potential at the surface of the conductor.

## 4. Can the potential inside a hollow spherical conductor ever be negative?

No, the potential inside a hollow spherical conductor cannot be negative. This is because the potential inside a conductor is always constant and equal to the potential at the surface of the conductor. Since the potential at the surface of a conductor is always positive, the potential inside a hollow spherical conductor will also be positive.

## 5. How do you determine the total charge on a hollow spherical conductor given the electric field and potential at a point outside the conductor?

To determine the total charge on a hollow spherical conductor, you can use the equation Q = -4πε0 * r2 * E, where ε0 is the permittivity of free space, r is the distance from the center of the conductor to the point where the electric field is being calculated, and E is the electric field at that point. This equation can be derived from the formula for the electric field outside a hollow spherical conductor and the equation V = k * Q / r.

Replies
23
Views
1K
Replies
1
Views
870
Replies
14
Views
895
Replies
22
Views
2K
Replies
8
Views
2K
Replies
2
Views
2K
Replies
21
Views
3K
Replies
8
Views
2K
Replies
3
Views
1K
Replies
19
Views
3K