Finding electric field vector given charge density, using Gauss's Law

In summary, the conversation discusses using Gauss' Law to find the vector electric field inside a long cylinder with a volume charge density proportional to the distance from the axis. The person attempted to solve for Qenc using the equation ∫vρv = Qenc but ran into issues with not knowing the boundary conditions. They mention that if the boundary conditions were known, they could solve for E using the equation Qenc/ε = EA. There is a question about the meaning of the 'v' in front of ρv.
  • #1
Lorenzoeblair
1
0

Homework Statement



A long cylinder carries a volume charge density which is proportional to the distance from the axis, ρv=0.005r. Find the vector electric field inside the cylinder using Gauss’ Law in integral form.


Homework Equations



∫E dot dA = Q/ε0
∫vρv = Qenc

The Attempt at a Solution



I first attempted trying to solve for Qenc using ∫vρv = Qenc, however I run to the issue of not know the boundary conditions. If I knew the boundary conditions, I would then set Qenc/ε = EA and solve for E.
 
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  • #2
Lorenzoeblair said:
∫vρv = Qenc

What do you mean with the 'v' in front of ρv?


ehild
 

Related to Finding electric field vector given charge density, using Gauss's Law

1. What is Gauss's Law?

Gauss's Law is a fundamental law in electrostatics that relates the electric field at a point to the charge enclosed by a surface surrounding that point. It 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.

2. How do I find the electric field using Gauss's Law?

To find the electric field at a point using Gauss's Law, you need to first choose a closed surface that encloses the point of interest. Then, calculate the electric flux through that surface by taking the dot product of the electric field and the surface area. Finally, set the flux equal to the enclosed charge divided by the permittivity of free space and solve for the electric field.

3. What is charge density?

Charge density is the amount of electric charge per unit volume in a given region of space. It can be expressed in units of coulombs per cubic meter or coulombs per square meter.

4. Can Gauss's Law be used for any charge distribution?

Yes, Gauss's Law can be used for any charge distribution, as long as the charge is enclosed by the chosen surface. However, it is most commonly used for symmetric charge distributions, such as a point charge or a charged sphere, as it simplifies the calculations.

5. What are the limitations of using Gauss's Law?

Gauss's Law is only applicable to static electric fields, meaning that it cannot be used for time-varying fields. It also assumes that the medium surrounding the charges is homogeneous and isotropic. Additionally, it is only valid for electrostatics and does not take into account the effects of moving charges or magnetic fields.

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