Charge Density from E-field

The dot product of the gradient operator with the E-field results in zero, indicating that the charge density in that region of space is also zero.
  • #1
AdkinsJr
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Homework Statement


I have a function for an E-field [tex]E(x,y,z,t)=E_o\cos(k(x-ct))\hat j[/tex] and I need to find the charge density...

Homework Equations



[tex]\vec \nabla \cdot\vec E=\frac{\rho}{\epsilon_o}[/tex]


The Attempt at a Solution




When I compute the dot product of gradient operator with the E-field I get zero since the only "term" in the factor is in the y direction, but it also does not have any variation with y so is the charge density in this region of space just zero?
 
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  • #2
AdkinsJr said:

Homework Statement


I have a function for an E-field [tex]E(x,y,z,t)=E_o\cos(k(x-ct))\hat j[/tex] and I need to find the charge density...

Homework Equations



[tex]\vec \nabla \cdot\vec E=\frac{\rho}{\epsilon_o}[/tex]


The Attempt at a Solution




When I compute the dot product of gradient operator with the E-field I get zero since the only "term" in the factor is in the y direction, but it also does not have any variation with y so is the charge density in this region of space just zero?

I would agree with that.
 

What is Charge Density from E-field?

Charge Density from E-field is a measure of the amount of electric charge in a given region of space, based on the strength of the electric field in that region.

How is Charge Density from E-field calculated?

Charge Density from E-field can be calculated by dividing the magnitude of the electric field by the permittivity of the medium in which the charge is located.

What is the relationship between Charge Density from E-field and electric field strength?

The Charge Density from E-field is directly proportional to the electric field strength. As the electric field strength increases, so does the charge density.

What are the units of Charge Density from E-field?

The units of Charge Density from E-field depend on the units of electric field and permittivity. In SI units, it is measured in coulombs per cubic meter (C/m3).

Why is Charge Density from E-field important in physics and engineering?

Charge Density from E-field is important because it helps us understand the behavior of electric fields and their effects on charged particles in a given space. It is also used in various engineering applications such as designing electrical circuits and analyzing the behavior of materials in electric fields.

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