Given Electric field, find the charge densities

In summary: R < 0In summary, the conversation is about a student seeking help with a physics homework problem involving finding the shape of a field and the charge density present. The student is able to identify that the field is completely spherical and is struggling with finding the density for the third term. The tutor suggests looking for a spherically symmetric charge distribution, such as a sphere with uniformly distributed charge, and the student eventually figures out the solution.
  • #1
ybisno
8
0
Homework Statement
Find the charge densities given the electric field (Attached question)
Relevant Equations
Electrostatics
Hi. Need help with physics homework. I was able to separate each term and find sigma from the second term and possibly lambda from the first term. Not sure how to approach the third term. (attached attempt at question)
 

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  • #2
Would you recognize the shape of the field if ##z_1 = 0## ?

(to begin with, for ##|\vec r| \ge R_2 ## :wink: )
 
  • #3
BvU said:
Would you recognize the shape of the field if ##z_1 = 0## ?

(to begin with, for ##|\vec r| \ge R_2 ## :wink: )
Yes its spherical right? could you guide me for the third term; how to find a density ?
 
  • #4
Completely spherical around ##\ (0,0,z_1)\ ##, yes
Any clue as to where there is no charge present ?
 
  • #5
No. We are currently looking to find either volume charge density or Q- charge density. That was the only hint I was given, the first two parts of my solution seem correct. Just the last term, I am struggling with.
 
  • #6
And no clue as to where there is charge present either ?

Made a sketch of E versus r ?
 
  • #7
BvU said:
And no clue as to where there is charge present either ?

Made a sketch of E versus r ?
Not really understanding your responses...
 
  • #8
  • #9
Yes, We have just started electrostatics. I used the concept of Gauss's differential form for the first section of my answer (the second term of the Electric field with the sign(z-z0).
 
  • #10
  • #11
BvU said:
Hard to help without giving it away completely.
You have a spherically symmetric field, so you are looking for a spherically symmetric charge distribution. Can it be, e.g., a sphere with uniformly distributed charge of a certain size ?
hmm so we would need to solve for Q (Uniform charge of the sphere) but would I need to split it into two cases? r>R and r<R?
 
  • #12
Is that really necessary ? What if R ##\downarrow 0 ## ?
 
  • #13
BvU said:
Is that really necessary ? What if R ##\downarrow 0 ## ?
I think i figured it out ! Thank you !
 
  • #14
Point charge at (0,0,z1)
 

1. How do you calculate charge density given an electric field?

The charge density can be calculated by dividing the magnitude of the electric field by the permittivity of the material. The equation is ρ = ε0 * |E|, where ρ is the charge density, ε0 is the permittivity, and |E| is the magnitude of the electric field.

2. What units are used to measure charge density?

The SI unit for charge density is coulombs per cubic meter (C/m^3), but it can also be measured in other units such as coulombs per liter (C/L) or coulombs per cubic centimeter (C/cm^3).

3. Can charge density be negative?

Yes, charge density can be negative. This indicates that the charge is distributed in a way that creates an electric field in the opposite direction of the given field.

4. How does the charge density affect the strength of the electric field?

The charge density is directly proportional to the strength of the electric field. This means that as the charge density increases, the electric field becomes stronger, and as the charge density decreases, the electric field becomes weaker.

5. What other factors can affect the charge density?

The charge density can also be affected by the type of material and its permittivity, as well as the distance from the source of the electric field. In some cases, the presence of other charges can also influence the charge density.

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