How Does a Uniform Electric Field Affect Charge Density Distribution?

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In summary: But if the electric field is not a constant, then the charge density can be anything, right? In summary, the conversation discusses the concept of divergence and how it relates to the charge density distribution in a space with a uniform electric field. The equation used to find the charge density is the divergence of the electric field, which is zero for a constant electric field. This means that the charge density in this space must also be zero.
  • #1
smantics
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Homework Statement


A space has an uniform electric field
E=(5.00 x 10^3 N/C)[itex]\widehat{x}[/itex] + (6.00 x 10^3 N/C)[itex]\widehat{y}[/itex] + (7.00 x 10^3 N/C)[itex]\widehat{z}[/itex].
Find the electric-charge density distribution p(r) in this space.


Homework Equations


u = (1/2)(εo)(E^2) , where εo is the constant called the permittivity of free space and = 8.85x10^-12 C^2/N*m^2

I used the equation above, but I was unsure if I was using the correct equation. I thought I maybe should have used one of Maxwell's equations instead: div*E=(ρ)/εo


The Attempt at a Solution


magnitude of Electric Field = sqrt((5.00 x 10^3 N/C)2 + (6.00 x 10^3 N/C)2 + (7.00 x 10^3 N/C)2)

magnitude of E = 10488.1 N/C

u = (1/2)(8.85x10^-12 C^2/N*m^2)(10488.1 N/C)^2
u = 4.87 x 10^-4 C/m^2

Is this the correct way to solve this problem?
 
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  • #2
smantics said:

Homework Statement


A space has an uniform electric field
E=(5.00 x 10^3 N/C)[itex]\widehat{x}[/itex] + (6.00 x 10^3 N/C)[itex]\widehat{y}[/itex] + (7.00 x 10^3 N/C)[itex]\widehat{z}[/itex].
Find the electric-charge density distribution p(r) in this space.

Homework Equations


u = (1/2)(εo)(E^2) , where εo is the constant called the permittivity of free space and = 8.85x10^-12 C^2/N*m^2

I used the equation above, but I was unsure if I was using the correct equation. I thought I maybe should have used one of Maxwell's equations instead: div*E=(ρ)/εo

The Attempt at a Solution


magnitude of Electric Field = sqrt((5.00 x 10^3 N/C)2 + (6.00 x 10^3 N/C)2 + (7.00 x 10^3 N/C)2)

magnitude of E = 10488.1 N/C

u = (1/2)(8.85x10^-12 C^2/N*m^2)(10488.1 N/C)^2
u = 4.87 x 10^-4 C/m^2

Is this the correct way to solve this problem?

No, u is an energy density. Use the Maxwell equation. What's the divergence of the constant electric field? You know what a divergence is, right?
 
  • #3
The divergence of a constant electric field is zero, right? I don't understand if the divergence is zero and the divergence is multiplied by the Electric field how you would get a proper answer.
 
  • #4
smantics said:
The divergence of a constant electric field is zero, right? I don't understand if the divergence is zero and the divergence is multiplied by the Electric field how you would get a proper answer.

Yes, the divergence of a constant E field is zero. The divergence of the field isn't multiplied by the E field. Go back and review 'divergence'. Maxwell's equation is telling you an easy thing about the charge density. What is it?
 
Last edited:
  • #5
So the divergence of an E field is basically taking partial derivatives with respect to x, y, and z of the E field, but since there are no variables in the E field that means the derivative of the constant E field is zero. Then since the constant E field has a divergence of zero, then does that mean that there cannot be a charge density distribution because the E field doesn't act like a source or a sink, and does that also mean that the charge density is also constant? The concept of divergence is really confusing to me.
 
  • #6
smantics said:
So the divergence of an E field is basically taking partial derivatives with respect to x, y, and z of the E field, but since there are no variables in the E field that means the derivative of the constant E field is zero. Then since the constant E field has a divergence of zero, then does that mean that there cannot be a charge density distribution because the E field doesn't act like a source or a sink, and does that also mean that the charge density is also constant? The concept of divergence is really confusing to me.

The equation is saying that if the divergence of the E field is zero, then the charge density must be zero, not just a constant, isn't it?
 
  • #7
So if the E field is zero and the charge density is also zero, and then does it even matter what the E field has numbers? As long as the E field is constant then the charge density will always be zero.
 
  • #8
smantics said:
So if the E field is zero and the charge density is also zero, and then does it even matter what the E field has numbers? As long as the E field is constant then the charge density will always be zero.

No, the numbers don't matter. Any constant field corresponds to zero charge density.
 

1. What is electric-charge density?

Electric-charge density is a physical quantity that measures the amount of electric charge per unit volume in a given space. It is denoted by the symbol ρ and has units of coulombs per cubic meter (C/m³).

2. How is electric-charge density calculated?

Electric-charge density is calculated by dividing the total electric charge in a given volume by the volume itself. This can be expressed as ρ = Q/V, where Q is the total charge and V is the volume.

3. What is the significance of electric-charge density?

Electric-charge density is an important concept in electromagnetism as it helps us understand the distribution of electric charges in a given space. It is also used in various equations to calculate electric fields and forces.

4. How does electric-charge density affect electric fields?

The electric-charge density in a particular region determines the strength of the electric field in that region. Higher charge density results in a stronger electric field, while lower charge density results in a weaker electric field.

5. How is electric-charge density related to electric potential?

Electric potential is the amount of work needed to move a unit of electric charge from one point to another in an electric field. Electric-charge density and electric potential are related through the equation V = kρ, where k is a constant and ρ is the electric-charge density.

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