# Electromagnetic Wave Equation

• outclassed
In summary, the conversation discusses the use of wave equations in a presentation and the confusion surrounding a specific equation involving the representation of electric field waves. The book suggests using Maxwell's equations and the separation of variables to derive the equation, but the spatial parts can be tricky. The correct equation is e^(i*stuff), not (e^i)*stuff. The conversation also mentions the importance of Maxwell's equations in physics.

#### outclassed

Hi I have a presentation tomorrow and have to explain a few wave equations. I am using a book to walk me through them but there is one point I don't understand:

At one point the book states:

Because k=(angular frequency)/c, we will represent the waves of the electric field as:

e^i (angular frequency ^ (x/c))

Now I am unsure what equation they used to get to this and also if its
e^i *(angular frequency ^ (x/c))
or
e^(i *(angular frequency ^ (x/c)))

Any help would be really great. I am sorry if this is a stupid question.
Drew.

to derive that, you need to use maxwell's equations and then separation of variables in 4 dimensions (3space 1time). The spatial parts are much trickier as i recall, if your familiar with math methods it won't be TOO bad to derive the time dependence.

Ok so the Maxwell equations, I am not familiar with those, I may just list it as a given and hope no one asks questions, do you know which of the two equations i listed it would be?
e^i * stuff or e^(i*stuff)?
Thanks again.

its e^(i*stuff) not (e^i)*stuff.
Maxwell's equations are some of the most important in all of physics; there are 4 (and a half... don't worry about that) and they describe the vast majority of all physical phenomena in the universe.

## 1. What is the electromagnetic wave equation?

The electromagnetic wave equation is a mathematical equation that describes the behavior of electromagnetic waves. It relates the electric and magnetic fields of an electromagnetic wave to each other and to the speed of light.

## 2. What are the variables in the electromagnetic wave equation?

The variables in the electromagnetic wave equation are the electric field (E), the magnetic field (B), the speed of light (c), and the position (x) and time (t) coordinates.

## 3. How is the electromagnetic wave equation derived?

The electromagnetic wave equation is derived from Maxwell's equations, which are a set of four equations that describe the behavior of electric and magnetic fields. It is a combination of the differential forms of these equations.

## 4. What is the significance of the speed of light in the electromagnetic wave equation?

The speed of light (c) is a fundamental constant in the electromagnetic wave equation. It represents the maximum speed at which all electromagnetic waves, including light, can travel in a vacuum. It also relates the electric and magnetic fields to each other, as they are both part of the same electromagnetic wave.

## 5. How is the electromagnetic wave equation used in real-world applications?

The electromagnetic wave equation is used in a wide range of real-world applications, including telecommunications, radar and satellite technology, and medical imaging. It allows scientists and engineers to predict and manipulate the behavior of electromagnetic waves, making it a crucial tool in modern technology.