How to find electric-charge density distribution

[smantics]

Given only an uniform electric field with unit vectors in the x, y, and z directions, how would you go about calculating the electric-charge density distribution p(r) for that electric field?

 

[Jolb]

One nice formula you might try applying is one of Maxwell's equations: $$\nabla \cdot \mathbf{E} = \frac {\rho} {\varepsilon_0}$$ The symbol $\rho$ is the charge density that generates the electric field $\mathbf{E}$, and $\varepsilon_0$ is a proportionality constant called the permittivity of free space.

 

[smantics]

Thanks, I will try that.

 

[mikeph]

The divergence of a uniform field is zero. There are no charges, at least where the field is uniform.

 

[sardar]

To calculate the electric-charge density distribution p(r) for a given uniform electric field with unit vectors in the x, y, and z directions, we can use the equation p(r) = ε0 * E(r), where ε0 is the permittivity of free space and E(r) is the electric field vector at a given point r. This equation relates the electric-charge density at a point to the electric field strength at that point.

To begin, we need to determine the magnitude and direction of the electric field at each point in space. This can be done by using the known unit vectors and the electric field equation, E = F/q, where F is the force exerted on a test charge q in the electric field. By varying the position of the test charge and measuring the resulting force, we can determine the strength and direction of the electric field at different points.

Once we have calculated the electric field vector at each point in space, we can plug these values into the equation p(r) = ε0 * E(r) to find the corresponding electric-charge density at each point. This will give us a distribution of electric-charge density throughout the space.

It is important to note that this method assumes a uniform electric field, meaning that the electric field strength and direction are constant throughout the space. If the electric field is not uniform, the calculation of the electric-charge density distribution will be more complex and may require additional equations and techniques.

In conclusion, to find the electric-charge density distribution for a given uniform electric field with unit vectors in the x, y, and z directions, we can use the equation p(r) = ε0 * E(r) by determining the strength and direction of the electric field at different points in space.