# Problem about electromagnetic waves -- Writing equations for B(t) and E(t)

• Bernat Pinos
In summary, the conversation is about finding the equations for the electric and magnetic fields for a plain electromagnetic wave with a 20GHz frequency, where the electric field is oriented along the Z axis and the amplitude is 10 V/m. The suggested approach is to find the most generic equation for the fields in 3D and then adapt it to the given conditions.
Bernat Pinos
Hi! I'm trying to solve a problem and I'm lost. Would someone kindly help me with the solution, please?

1. Homework Statement

A plain electromagnetic wave with a 20GHz frequency moves in the positive direction of the Y axis and its magnetic field is oriented along the Z axis. The amplitude of the electric field is 10 V / m, and the electric field at the origin of coordinates is 10 V / m when t = 0. Write the equation for E and for B.

## Homework Equations

B = -(Em/c)*sin(ky + ωt)x

B = Bm*cos(kx - ωt)

E = Em*cos(kx - ωt)

## The Attempt at a Solution

As I said I'm really lost, so my attemps have been almost nothing.

Thanks!

Bernat Pinos said:

## Homework Equations

B = -(Em/c)*sin(ky + ωt)x

B = Bm*cos(kx - ωt)

E = Em*cos(kx - ωt)
What is the most generic equation you can find for the electric and magnetic field in 3D?

Once you have that, you simply need to adapt it to the conditions specified.

Bernat Pinos
DrClaude said:
What is the most generic equation you can find for the electric and magnetic field in 3D?

Once you have that, you simply need to adapt it to the conditions specified.

## 1. What are electromagnetic waves?

Electromagnetic waves are a type of energy that is made up of electric and magnetic fields. They are produced by the movement of electrically charged particles and can travel through space without the need for a medium.

## 2. What are the equations for B(t) and E(t)?

The equations for B(t) and E(t) are as follows:
B(t) = B0cos(ωt - kx)
E(t) = E0cos(ωt - kx + φ)
Where B0 and E0 are the amplitudes of the magnetic and electric fields, ω is the angular frequency, k is the wave number, x is the position, and φ is the phase shift.

## 3. How do these equations relate to electromagnetic waves?

These equations represent the oscillating behavior of the electric and magnetic fields in an electromagnetic wave. They show that the fields are perpendicular to each other and to the direction of wave propagation, and that they vary sinusoidally with time and position.

## 4. What is the significance of the constants in these equations?

The constants in these equations have specific values that determine the properties of the electromagnetic wave. For example, the amplitude of the electric and magnetic fields determines the intensity of the wave, while the angular frequency and wave number determine the wavelength and frequency of the wave.

## 5. Are there any real-life applications of these equations?

Yes, these equations are used in many practical applications, such as communication technology (radio, television, and cell phones), medical imaging (MRI), and energy production (solar panels). They also form the basis for understanding the behavior of light and other types of electromagnetic radiation.

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