Given Electric field, find the charge densities

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SUMMARY

The discussion focuses on determining charge densities from an electric field, specifically in the context of electrostatics and Gauss's law. The user successfully identified the spherical symmetry of the electric field and explored the implications for charge distribution. Key concepts include the use of Gauss's differential form and the consideration of cases for charge density based on the radius relative to the charge distribution. Ultimately, the user concluded that the charge configuration could be modeled as a point charge located at (0,0,z1).

PREREQUISITES
  • Understanding of Gauss's law in electrostatics
  • Familiarity with electric field concepts and charge distributions
  • Knowledge of spherical symmetry in physics
  • Basic calculus for solving differential equations
NEXT STEPS
  • Study the application of Gauss's law in various charge configurations
  • Learn about spherical charge distributions and their electric fields
  • Explore the concept of volume charge density and its calculations
  • Investigate the implications of point charges in electrostatics
USEFUL FOR

Students of physics, particularly those studying electrostatics, as well as educators and anyone interested in understanding charge densities and electric fields.

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

(to begin with, for ##|\vec r| \ge R_2 ## :wink: )
 
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 ?
 
Completely spherical around ##\ (0,0,z_1)\ ##, yes
Any clue as to where there is no charge present ?
 
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.
 
And no clue as to where there is charge present either ?

Made a sketch of E versus r ?
 
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...
 
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)
 

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