Electric Fields, Flux, Gauss' Law

In summary, the conversation discusses the use of Gauss' law to determine the unknown charge distribution p and total charge q_tot. The formula for the electric field E produced by p is given, and the forum member attempts to use Gauss' law in differential form to determine p. They calculate the divergence incorrectly and are directed to look up the correct formula for spherical coordinates. They also attempt to integrate over p to find q_tot, but struggle to determine the appropriate limits and the meaning of dV in spherical coordinates.
  • #1
jajay504
12
0

Homework Statement


The Electric field E produced by an unknown charge distribution p (rho) is E(r)= (constant)*((exp(-ar))/r^2)*(r_hat).
a.) Use Gauss' law in differential for to determine p(rho)
b.) Find the total charge q_tot by directly integrating p(rho), and show that it is 0.
c.) Find q_tot again, except this time use Gauss' law in integral form.
d.) Make a sketch of p(rho)

Homework Equations





The Attempt at a Solution

 
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  • #2
According to the forum rules, you need to show some effort at working the problem yourself before you can receive help.
 
  • #3
Hey! Sorry for that... I did some work but I got stuck.

I used divergence E = p/e0

a.) div E = (-a/r^2 - 2/r^3) * exp(-a*r) = p/e0. So I know what p is.
b.) Then I tried to integrate over p(rho) to get q_tot

q_tot = Integral [pdV]
I got --> exp(-a*r)/r^2 - 2*exp(-a*r)/r^3 = q_tot

I'm still trying to figure out what is this surface
 
  • #4
vela said:
According to the forum rules, you need to show some effort at working the problem yourself before you can receive help.

Sorry for that! I put down the work I had
 
  • #5
jajay504 said:
Hey! Sorry for that... I did some work but I got stuck.

I used divergence E = p/e0

a.) div E = (-a/r^2 - 2/r^3) * exp(-a*r) = p/e0. So I know what p is.
You calculated the divergence incorrectly. Look up the formula for the divergence in spherical coordinates. Your book should have a list of the various vector operators for different coordinate systems.
b.) Then I tried to integrate over p(rho) to get q_tot

q_tot = Integral [pdV]
I got --> exp(-a*r)/r^2 - 2*exp(-a*r)/r^3 = q_tot

I'm still trying to figure out what is this surface
It's not a surface; it's a volume. What is dV in spherical coordinates? What limits should you be integrating over?

Please show more details of your work.
 

1. What is an electric field?

An electric field is a force field that surrounds a charged particle. It is created by a charged object and exerts a force on other charged objects within its range.

2. How is electric field strength measured?

Electric field strength is measured in newtons per coulomb (N/C). This represents the amount of force exerted on a charged particle per unit of charge.

3. What is flux?

Flux is a measure of the flow of a vector field through a surface. In the context of electric fields, flux is the amount of electric field passing through a surface.

4. What is Gauss' Law?

Gauss' Law is a fundamental law in electromagnetism that relates the electric flux through a closed surface to the enclosed electric charge. It states that the total electric flux through a closed surface is equal to the charge enclosed by that surface divided by the permittivity of free space.

5. How is Gauss' Law used to calculate electric fields?

Gauss' Law can be used to calculate electric fields by using the symmetry of the charge distribution and choosing a Gaussian surface that encloses the charge. The electric field can then be calculated by using the equation E = Q/ε_0A, where Q is the enclosed charge, ε_0 is the permittivity of free space, and A is the area of the Gaussian surface.

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