Electric field with constant direction

In summary, the conversation discusses an electric field with a constant value in one direction, and the question of how this can occur with a homogenous charge density. The possibility of a charged body with infinite thickness and height is considered, and it is noted that the solution for the electric field depends on the boundary conditions.
  • #1
Grieverheart
31
0
I just started Classical Electrodynamics and stumbled upon a problem:

An electric field has this form:

[tex]E_{x}=ax ,E_{y}=0 ,E_{z}=0[/tex]

where a is a constant.Find the density of the charge(ok that's easy).How do you explain that the field points towards a constant direction although the density of the charge is homogene?

Ok,so I though maybe the charged body is like mug with infinite thickness and an infinite hight.Is this correct?Is there a way to find the answer mathematically?
 
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  • #2
The charge density is constant, but the solution to the PDE div E=a is not unique.
The solution for E also depends on the boundary conditions.
In this case the BC as x, y, and -->infinity determines E.
 
  • #3


The direction of an electric field is determined by the distribution of charges in space. In this case, the electric field has a constant direction in the x-direction because the charges are distributed along the x-axis. This does not necessarily mean that the charge density is constant, as there could be variations in the charge distribution along the x-axis.

To find the charge density, you can use Gauss's Law, which states that the electric flux through a closed surface is equal to the charge enclosed by that surface. In this case, you can choose a Gaussian surface that is perpendicular to the x-axis and encloses the charged body. Then, by integrating the electric field over the surface, you can find the charge enclosed and calculate the charge density.

As for your analogy of a mug with infinite thickness and height, it is not entirely accurate as the distribution of charges in this case is not continuous. However, it can help visualize the concept of a constant electric field in a certain direction.

In order to find the answer mathematically, you can use the equations of electrostatics and Maxwell's equations to solve for the electric field and charge density. This may involve solving differential equations and using boundary conditions to determine the behavior of the electric field in the given scenario.

Overall, the direction of an electric field is determined by the distribution of charges, and a constant direction does not necessarily mean a constant charge density. Mathematically, the charge density can be found by using Gauss's Law and solving for the electric field using appropriate equations and boundary conditions.
 

1. What is an electric field with constant direction?

An electric field with constant direction is a region in space where electrically charged particles experience a force in the same direction at all points. This means that the magnitude and direction of the electric field do not change as you move from one point to another.

2. How is an electric field with constant direction created?

An electric field with constant direction is created by placing two oppositely charged objects near each other. The electric field lines extend from the positive charge to the negative charge, and the direction of the field is always from positive to negative.

3. What is the difference between an electric field with constant direction and a changing electric field?

The main difference between an electric field with constant direction and a changing electric field is that in a constant electric field, the magnitude and direction of the field do not change, while in a changing electric field, they can vary at different points in space. Additionally, a constant electric field is often created by stationary charged objects, while a changing electric field is usually associated with moving charged objects.

4. How is the strength of an electric field with constant direction measured?

The strength of an electric field with constant direction is measured by the electric field strength, also known as the electric field intensity. This is a vector quantity that is measured in newtons per coulomb (N/C). It represents the force experienced by a unit positive charge placed in the electric field.

5. What are some real-world applications of an electric field with constant direction?

An electric field with constant direction has many practical applications, such as in electronic devices, where it is used to control the flow of electrons. It is also used in electrostatic precipitators to remove pollutants from industrial exhaust gases, and in particle accelerators to manipulate charged particles. The Earth's magnetic field can also be thought of as a constant electric field, which protects us from harmful solar radiation.

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