# Electric field for a plane wave in free space

• jb646
In summary, the conversation discusses a problem involving the electric field for a plane wave in free space. The problem asks for the statement and relationship between w and ka in the wave equation, the direction of wave propagation, an expression for the accompanying magnetic field, and verification that the given electric field satisfies the wave equation. The conversation also mentions relevant equations and suggests using Wikipedia for further assistance.
jb646
This isn't really a homework problem, I just need to know how to do a problem similar to this one for the final and I don't want to fail, so I posted it here.

The problem is:
Given the electric field for a plane wave in free space: E(r,t)=E1cos(wt-ky)k
a)what is the statement for w and ka in the wave equation and how are they related to each other?
b)what is the direction of wave propagation?
c)write an expression for the accompanying magnetic field B
d)show that the electric field given above is is satisfied with the wave equation

relevant equations: since this is more of an explanation problem I worked the equations into the attempt at a solution

a)do I have to rearrange the equations to solve for w and k or do I just integrate to solve for them?

b)im pretty sure it is in the x-direction, that makes sense to me

c)∇xE=-(∂B/∂t)
so do I just calculate the cross products:
x y z
d/dx d/dy d/dz
E1cos(wt-ky) 0 E2cos(wt-ky)

and set that equal to -(∂B/∂t), if so, how to I un-partialize it [can you tell I'm not really a physics major, just taking a required class...sorry for the lack of terminology and general knowledge]

a) I think part a just wants you to say what omega and k are, i.e. k is the wave propagator and omega is angular frequency. Though by all means, rearrange so that you have it in terms of wavelength and displacement.

b) What physical reason do you have to believe it's propagating in the x-direction?

c) For a plane wave, remember that the magnetic field is orthogonal to the electric field with a factor of c.

I think this wikipedia entry will greatly help you with this problem.

## 1. What is an electric field for a plane wave in free space?

The electric field for a plane wave in free space is a type of electromagnetic field that is characterized by oscillating electric and magnetic fields that propagate through space in a specific direction. It is a fundamental concept in electromagnetism and is used to describe the behavior of light and other electromagnetic waves.

## 2. How does the electric field for a plane wave in free space differ from other types of electric fields?

The main difference is that the electric field for a plane wave in free space is a transverse wave, meaning that the direction of its oscillations is perpendicular to the direction of its propagation. This is in contrast to other types of electric fields, such as that of a static charged particle, which is a longitudinal wave.

## 3. What factors affect the strength of the electric field for a plane wave in free space?

The strength of the electric field for a plane wave in free space is affected by the amplitude of the wave, the distance from the source, and the angle at which the wave is observed. It is also influenced by the properties of the medium through which it is propagating, such as its permittivity and conductivity.

## 4. How is the electric field for a plane wave in free space represented mathematically?

The electric field for a plane wave in free space is typically represented by a sinusoidal function, in which the electric field varies as a function of time and position. Mathematically, it can be described using Maxwell's equations, which relate the electric and magnetic fields to each other.

## 5. What are some practical applications of the electric field for a plane wave in free space?

The electric field for a plane wave in free space has numerous practical applications in modern technology. It is used in telecommunications for wireless communication, in radar systems for remote sensing, and in medical imaging techniques such as MRI. It is also essential in understanding the behavior of light and other electromagnetic waves in nature.

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