Solving Gauss's Law Problem: Determine Electric Field on/in Sphere

In summary, the conversation discusses a problem with understanding Gauss's law and determining the electric field at the surface and inside of a metallic sphere with a given charge. It also brings up the concept of electrostatic equilibrium and the distribution of charge on a conductor's surface.
  • #1
samblue
22
0

Homework Statement



Ok so I', having some problems with Gauss's law. I know what it is, but I still can't get the answers right.

A metallic sphere of diameter 2*10-2m has been given a charge of 2 nC. State Gauss's law. Use this to determine the electrical field at the surface of the sphere. What is the electrical field inside the field?


Homework Equations



integral (E.dA)=Qenclosed/permitivity of free space


The Attempt at a Solution



the fist part is the equation written below.

However I am not sure about the next part. How do I distinguish between the charge inside the spehere and the charge on the surface?

Thanks
 
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  • #2
Assuming electrostatic equilibrium, what's the charge inside a conductor?
 
  • #3
Doc Al said:
Assuming electrostatic equilibrium, what's the charge inside a conductor?


Not really sure. Is it zero? Becasue all of the charge passes through it?
 
  • #4
samblue said:
Not really sure. Is it zero? Becasue all of the charge passes through it?
Key fact (where electrostatic equilibrium holds): The electric field is zero everwhere inside a conductor. All the (net) charge on a conductor lies on its surface.
 
  • #5
thanks
 

FAQ: Solving Gauss's Law Problem: Determine Electric Field on/in Sphere

What is Gauss's Law and why is it important in solving electric field problems?

Gauss's Law is a fundamental law in electromagnetism that relates the electric flux through a closed surface to the charge enclosed by that surface. It is important in solving electric field problems because it provides a simple and elegant way to calculate the electric field in a given region, without having to consider the individual contributions of all the charges in that region.

How do you determine the electric field on a spherical surface using Gauss's Law?

To determine the electric field on a spherical surface using Gauss's Law, you first need to choose a Gaussian surface that is symmetric with respect to the charge distribution. This could be a sphere, a cylinder, or a cube, depending on the situation. Then, you need to calculate the electric flux through this surface, which is given by the product of the electric field and the surface area of the Gaussian surface. Finally, you can use Gauss's Law, which states that the electric flux through a closed surface is equal to the charge enclosed by that surface divided by the permittivity of free space, to solve for the electric field.

What are the necessary conditions for using Gauss's Law to solve electric field problems?

There are three important conditions that need to be met in order to use Gauss's Law to solve electric field problems. First, the electric field must be constant and have the same magnitude and direction at every point on the Gaussian surface. Second, the Gaussian surface must be closed, meaning that it encloses a certain volume and there are no gaps or holes in the surface. Third, the charge distribution must be symmetric with respect to the Gaussian surface, so that the electric field is also symmetric.

Can Gauss's Law be used to determine the electric field inside a charged sphere?

Yes, Gauss's Law can be used to determine the electric field inside a charged sphere. In this case, the Gaussian surface would be a concentric sphere with the same center as the charged sphere. Since the electric field inside the charged sphere is not affected by the distribution of charges on the surface, the charge enclosed by the Gaussian surface will be equal to the total charge of the sphere. This allows us to use Gauss's Law to calculate the electric field at any point inside the sphere.

What are some common mistakes when solving Gauss's Law problems?

One common mistake when solving Gauss's Law problems is not choosing the correct Gaussian surface. It is important to carefully analyze the situation and choose a surface that is symmetric and encloses the desired region. Another mistake is not considering the direction of the electric field, which can lead to incorrect calculations. It is also important to keep track of units and make sure they are consistent throughout the problem. Lastly, it is crucial to check the overall solution to ensure it makes sense and is physically reasonable.

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