NONUNIFORM Vol. Charge Density - V at the center of sphere

In summary, the conversation is about finding the potential at the center of a sphere with volume charge density of rho(r) = rho_0 * R/r and the use of Gauss's Law to solve the problem. One person is struggling to find the correct answer and is seeking hints and confirmation on their solution.
  • #1
JamesTheBond
18
0
This should be easy, but for some odd reason I am not getting the right answer.

Assuming the potential V=0 at infinity, what is the V at the center of a sphere with volume charge density rho(r) = rho_0 * R/r

I keep getting (integral from 0 to R K*(4*pi*rho_0)*R/2) which I don't think is right.

Does anyone have any hints which will help me out here?
 
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  • #2
Your integrand is constant? That's not good. Unfortunately you didn't post enough of your work for me to have any idea of where you are going wrong. I think you want to use the homework form as well.
 
  • #3
I did the problem again, now I have: V_0 = k*Q/R = k*4*pi*rho_0*R^2/2 = rho_0*R^2/(2*epsilon_0)

Can anyone confirm if I did this right?
 
  • #4
Try finding the spherical E in terms of charge density using Gauss's Law. Then integrate that in terms of dr from R to 0
 

FAQ: NONUNIFORM Vol. Charge Density - V at the center of sphere

What is nonuniform volume charge density?

Nonuniform volume charge density refers to the distribution of electric charge within a given volume that is not uniform or evenly distributed. This means that the charge is concentrated in certain areas and sparse in others.

How is nonuniform volume charge density measured?

Nonuniform volume charge density is typically measured in coulombs per cubic meter (C/m^3). This unit represents the amount of electric charge per unit volume.

What factors can affect nonuniform volume charge density?

Nonuniform volume charge density can be affected by a variety of factors, including the shape and size of the object, the type and distribution of the material, and the presence of external electric fields.

How does nonuniform volume charge density impact electric fields?

The nonuniform distribution of electric charge within a volume can lead to variations in the strength and direction of electric fields. This can affect the movement and behavior of charged particles within the field.

What is the significance of calculating the electric potential at the center of a sphere with nonuniform volume charge density?

Calculating the electric potential at the center of a sphere with nonuniform volume charge density can provide important insights into the behavior of electric fields and the distribution of electric charge within a given volume. This information can be useful in understanding and predicting the behavior of electrically charged systems.

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