# Electric field as a function of time

• jasonchiang97
In summary, the conversation discusses the concept of superposition in classical physics and its application to an electromagnetic wave propagating in the z-direction. The electric field vector of the wave is a superposition of two linearly polarized waves, Ex and Ey, which are described by the equations Ex = a cos(kz − ωt) and Ey = b cos(kz − ωt + δ). The parameter δ represents the phase difference between the two components. At a fixed value of z, the electric fields Ex and Ey can be described as a function of time.

## Homework Statement

Before diving into the quantum-mechanical superposition principle, let’s get some practice with superposition in classical physics. Consider an electromagnetic wave propagating in the z-direction, which is a superposition of two linearly polarized waves. The electric field vector in the wave is E = Ex + Ey, where Ex = a cos(kz − ωt), Ey = b cos(kz − ωt + δ). (1) The parameter δ is a real number between −π/2 and π/2, and indicates by how much the two components are out of phase. Look at the behavior of the electric field at some fixed value of z, say z = 0 for simplicity.

a) [2pt] Describe what the electric fields Ex and Ey are doing as a function of time.

E = Ex + Ey

## The Attempt at a Solution

Well I'm not really sure how to start the problem so I just tried to put it into complex form

Ex = a*ei(kz-ωt)/SUP]
Ey = b*ei(kz-ωt + δ)

Since they are separate components, I cannot add them together so I am unsure of what to do next

jasonchiang97 said:
so I just tried to put it into complex form
Making things difficult, eh ? Why do so if you have an expression for ##E_x## and for ##E_y## as a function of ##z## and ##t## and the first part of the exercise asks for ##E_x## and ##E_y## as a function of ##t## for a given ##z## ?

Things may be more complex in part b) but I can't guess and you don't tell ...

BvU said:
Making things difficult, eh ? Why do so if you have an expression for ##E_x## and for ##E_y## as a function of ##z## and ##t## and the first part of the exercise asks for ##E_x## and ##E_y## as a function of ##t## for a given ##z## ?

Things may be more complex in part b) but I can't guess and you don't tell ...

Ah, so I can just set z=0 and I would have my function?

Bingo

## What is an electric field as a function of time?

An electric field is a physical quantity that describes the strength and direction of the force exerted on an electrically charged particle. As a function of time, it represents how the electric field changes over time.

## How is an electric field as a function of time calculated?

The electric field as a function of time can be calculated using the equation E(t) = F/q, where E is the electric field, F is the force exerted on the charged particle, and q is the magnitude of the charge.

## What factors affect the electric field as a function of time?

The electric field as a function of time is affected by the magnitude and direction of the charge, as well as the distance between the charged particles. It can also be influenced by the presence of other electrically charged objects or the movement of the charged particles.

## How does the electric field as a function of time relate to electromagnetic waves?

An electric field as a function of time is an essential component of electromagnetic waves. As the electric field oscillates, it creates a changing magnetic field, and together, these fields propagate through space as electromagnetic waves.

## What are some real-world applications of understanding the electric field as a function of time?

Understanding the electric field as a function of time is crucial in many areas, including telecommunications, power generation and distribution, and medical imaging. It is also essential in studying and predicting weather patterns and space weather phenomena.