# Relationship between electric field components: ellipse

• boddhisattva
In summary, an ellipse is a geometric shape used to represent the relationship between the x and y components of an electric field. This shape can be described by the equation E<sub>x</sub>^2/a^2 + E<sub>y</sub>^2/b^2 = 1, where a and b are constants that determine the strength and orientation of the electric field. An ellipse can represent any type of electric field, including uniform, non-uniform, and non-constant fields. The shape of an ellipse can change depending on the strength and orientation of the electric field, resulting in either a narrower and more elongated ellipse or a wider and more circular one. The relationship between electric field components in an ellipse is unique
boddhisattva

## Homework Statement

Given an electric field:

E=Ex*ex+Ey*ey

with

Ex=cos(kx-wt)
Ey=cos(kx-wt+e)

where e is the phase difference

Show that

Ex^2 + Ey^2 - 2*Ex*Ey*cos(e) = ( sin(e) )^2

Ex=cos(kx-wt)
Ey=cos(kx-wt+e)

## The Attempt at a Solution

Was unable to find a solution with trigonometric relations

That equation can't possibly be true. The units on the two sides don't match.

## 1. What is an ellipse in the context of electric fields?

An ellipse is a geometric shape that describes the relationship between the x and y components of an electric field. It represents the path of a charged particle moving through the electric field.

## 2. How are the electric field components related in an ellipse?

The x and y components of an electric field in an ellipse are related by the equation Ex^2/a^2 + Ey^2/b^2 = 1, where a and b are constants related to the strength and orientation of the electric field.

## 3. Can an ellipse represent any type of electric field?

Yes, an ellipse can represent any type of electric field, including uniform, non-uniform, and even non-constant fields.

## 4. How does the shape of an ellipse change with different electric field configurations?

The shape of an ellipse can change depending on the strength and orientation of the electric field. A stronger or more focused electric field will result in a narrower and more elongated ellipse, while a weaker or more dispersed electric field will result in a wider and more circular ellipse.

## 5. How does the relationship between electric field components in an ellipse differ from other geometric shapes?

The relationship between electric field components in an ellipse is unique in that it allows for a wide range of configurations and can represent both uniform and non-uniform electric fields. Other geometric shapes, such as circles or squares, have more specific relationships between their components that may not be applicable to all types of electric fields.

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