# Request Assistance with Gauss's Law- Surface charge of sphere

• chipperh
In summary, the surface charge on the exterior of the spherical shell will be inversely proportional to the charge at the center of the sphere. This will result in a (negative) electric field around the exterior of the shell.
chipperh

## Homework Statement

a 240nC point charge is placed at the center of an uncharged spherical consucting shell 20cm in radius. A) What is the surface charge density on the outer surface of the shell? B) What is the electric field strength at the shell's outer surface?

## Homework Equations

A) Charge Density=surface charge/surface area.
B) E=q/(4*pi*E*r^2)

I am unsure if surface charge is the same as the "E" calculated in Part 'B". If it isn't, how do I calculate Surface charge.

## The Attempt at a Solution

A) 107330c/m^2 (Doesn't seem correct)
B) results are 53950n/C

Thank you.
Chip

Surface charge is simply the collective charge on the surface of the sphere (meaning q). The electric field around the surface is E = surface charge density/permittivity of free space.

chipperh said:

## Homework Statement

a 240nC point charge is placed at the center of an uncharged spherical consucting shell 20cm in radius. A) What is the surface charge density on the outer surface of the shell? B) What is the electric field strength at the shell's outer surface?

## Homework Equations

A) Charge Density=surface charge/surface area.
B) E=q/(4*pi*E*r^2)

I am unsure if surface charge is the same as the "E" calculated in Part 'B". If it isn't, how do I calculate Surface charge.

## The Attempt at a Solution

A) 107330c/m^2 (Doesn't seem correct)
B) results are 53950n/C

Thank you.
Chip

Because the spherical shell is conducting, in the steady state the electric field in the interior of the shell must be zero. That means that there will be a sufficient surface charge on the interior of the shell to cancel the point charge [lace in the center. Since the conducting shell is neutral, there will be an equal and (opposite sign) surface charge on the outside surface of the shell. The magnitude of these surface charges will have something to do with the magnitude of the charge at the center. If you think about it a bit, you'll also be able to quickly figure out the magnitude of the electric field at the outer surface of the conducting shell.

Ahhhh! Thank you. I appreciate the guidance in the correct direction.

My cognitive friction is a result of taking one or two college classes at a time, hence, many classes that are taken during the same semester for full time students are spread out by a few years for me. I have to recall or re-study certain principles, rules and/or methods.

Chip

## 1. What is Gauss's Law and how does it relate to surface charge of a sphere?

Gauss's Law is a fundamental law in electromagnetism that relates the electric flux through a closed surface to the total charge enclosed by that surface. It can be used to calculate the electric field and surface charge of a sphere by considering the symmetry of the sphere and the distribution of charge on its surface.

## 2. How do I calculate the surface charge of a uniformly charged sphere using Gauss's Law?

To calculate the surface charge of a uniformly charged sphere, you can use the formula q = 4πε₀r²E, where q is the total charge on the sphere, ε₀ is the permittivity of free space, r is the radius of the sphere, and E is the electric field at the surface of the sphere. This formula can be derived using Gauss's Law and the symmetry of the sphere.

## 3. Can Gauss's Law be used for non-uniformly charged spheres?

Yes, Gauss's Law can still be used for non-uniformly charged spheres. However, the calculation of surface charge becomes more complicated as the distribution of charge on the sphere is not uniform. In these cases, you would need to use a differential form of Gauss's Law and integrate over the surface of the sphere to find the surface charge.

## 4. What is the significance of the electric field at the surface of a charged sphere?

The electric field at the surface of a charged sphere is directly related to the surface charge of the sphere. This means that the surface charge can be controlled by adjusting the electric field, which can be useful in various applications such as controlling the motion of charged particles or designing electronic devices.

## 5. Can Gauss's Law be used for other shapes besides spheres?

Yes, Gauss's Law can be applied to any shape as long as it has some symmetry. However, the calculation becomes more complex for non-spherical shapes as you would need to consider the shape and orientation of the surface and the distribution of charge on it. For simpler shapes, such as cylinders or planes, Gauss's Law can still be applied using the same principles as for a sphere.

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