# Calculating a Non-Uniform Electric Field Given 6 different Electrode Pairs

• penguino6971
In summary, the speaker is seeking help in finding the electric field for a scenario that does not apply to Gauss' Law. They have attempted to use individual elements and Gauss' Law, but it proved to be inefficient and potentially incorrect. The suggested solution is to solve the Laplace equation and use the gradient of the electric potential to calculate the electric field. This approach will require boundary conditions and a numerical solution is recommended.
penguino6971
Homework Statement
I have been asked to find the most non-uniform electric field generated by the electrode pairs below given a range of frequencies, voltages, and distances between the electrode pairs. I intend to use a program such as Matlab to run various frequencies, distances, and voltages and then graphing the results to see the most non-uniform electric field. However, due to the unique design of the electrode pairs, I have no idea on where to start and how frequency relates to the electric field.
Relevant Equations
V = E*d
I know how to find the electric field of more traditional designs i.e. a sphere, through Gauss' Law but I don't think Gauss' Law applies to this scenario. I tried to separate each part of the electrode into simple spheres and rods and using Gauss' Law to find these individual elements. This proved to inefficient and could be very much incorrect. Any help would be appreciated.

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If you can't make use of Gauss' law for this problem, then you may need to resort to solving the Laplace equation, which will give you the electric potential. From this, you can then calculate the electric field using the gradient of the electric potential. Note that this will require boundary conditions, and a numerical solution is likely the only approach that can be taken.

## 1. How do you calculate a non-uniform electric field?

To calculate a non-uniform electric field, you will need to know the charges and positions of the six different electrode pairs. Then, you can use the formula E = k*q/r^2 to calculate the electric field at any point in space, where k is the Coulomb's constant, q is the charge, and r is the distance between the point and the charge.

## 2. What is the difference between a uniform and non-uniform electric field?

A uniform electric field has the same strength and direction at every point in space, while a non-uniform electric field has varying strength and direction at different points in space. In other words, a uniform electric field has constant electric field lines, while a non-uniform electric field has curved or distorted electric field lines.

## 3. What factors affect the strength of a non-uniform electric field?

The strength of a non-uniform electric field is affected by the charges and positions of the electrode pairs. The closer the charges are to each other, the stronger the electric field will be. Additionally, the magnitude of the charges also plays a role in determining the strength of the electric field.

## 4. Can you give an example of a non-uniform electric field?

One example of a non-uniform electric field is the electric field between two parallel plates with opposite charges. The electric field is stronger near the edges of the plates and weaker in the middle, resulting in a non-uniform electric field.

## 5. How can calculating a non-uniform electric field be useful?

Calculating a non-uniform electric field can be useful in understanding and predicting the behavior of electric charges in a given system. It can also be used in designing and optimizing electrical devices, such as capacitors and sensors.

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