Wavelength of an Electromagnetic wave

• rohanprabhu
In summary: Assuming the sheet is very thin and doesn't have any external fields to compete with, the radiation intensity at a distance from the sheet is proportional to the square of the current intensity.
rohanprabhu
I tried to see how we go about *creating* and electromagnetic wave. To do that, I take a charge 'Q' rotating in a circle of 'radius' r in the y-z plane, with it's center as the origin with an angular velocity $\omega$. The electric field at a point (x, y, z) is given by:

$$E(x, y, z) = E_x(x, y, z) + E_y(x, y, z) + E_z(x, y, z)$$

where:

$$E_x(x, y, z) = \frac{Q(9 \times 10^{9})x}{\left(r^2+x^2+y^2+z^2-2 r (y \text{Cos}[t \omega ]+z \text{Sin}[t \omega ])\right)^3}\hat{i}$$

$$E_y(x, y, z) = \frac{Q(9 \times 10^{9})(y - r\text{Cos}[t \omega ])}{\left(r^2+x^2+y^2+z^2-2 r (y \text{Cos}[t \omega ]+z \text{Sin}[t \omega ])\right)^3} \hat{j}$$

$$E_z(x, y, z) = \frac{Q(9 \times 10^9)(y - r\text{Sin}[t \omega ])}{\left(r^2+x^2+y^2+z^2-2 r (y \text{Cos}[t \omega ]+z \text{Sin}[t \omega ])\right)^3} \hat{k}$$

Is this an electromagnetic wave. I think it is because well.. since the charge retraces it's path every $$t = \frac{2\pi}{\omega}$$.. so the electric field at any point will vary periodically as a function of time.

How do I find it' wavelength and frequency? Is $$f = \frac{1}{T} = \frac{\omega}{2\pi}$$ correct for frequency?

Also.. how do i find the generated magnetic field? And assuming that the wavelength of this wave comes out to be something within the visible range of light.. will this moving charge cause visible radiation?

You have just tried to use the electrostatic E.
Generating an EM wave is much more complicated, involving the retarded time and Maxwell's equations. You have to read the EM radiation chapter in a more advanced text.

pam said:
You have just tried to use the electrostatic E.
Generating an EM wave is much more complicated, involving the retarded time and Maxwell's equations. You have to read the EM radiation chapter in a more advanced text.

any recommendations?

Also.. Maxwell did say that a changing electric field causes a changing magnetic field. In that case, the electric field which i presented, should also create a magnetic field. So, basically i have a time changing vector field consisting of both and electric field and a magnetic field.. so why is it not an electromagnetic wave?

See for example chapter 9 of Griffiths's "Introduction to Electrodynamics."

The first example most books do is radiation from an oscillating dipole: a positive and negative charge "flip-flopping" back and forth in simple harmonic motion. A Google search on "dipole radiation" or something similar might turn up some lecture notes.

Dipole radiation is a pretty hard case to analyze. A much simpler case for radiation is an infinite sheet with oscillating current. If the current density is 1 amp/meter (yes, those are the units for sheet current, not amps/meter squared!) then you create a field at right angles of 377 volts/meter and an associated power of 377 watts flowing away from the sheet.

1. What is the definition of wavelength?

The wavelength of an electromagnetic wave is the distance between two consecutive peaks or troughs of the wave. It is typically represented by the Greek letter lambda (λ) and is measured in meters (m).

2. How is wavelength related to frequency?

Wavelength and frequency are inversely proportional to each other. This means that as the wavelength decreases, the frequency increases and vice versa. This relationship is described by the equation: wavelength = speed of light / frequency.

3. What is the relationship between wavelength and energy?

The energy of an electromagnetic wave is directly proportional to its frequency and inversely proportional to its wavelength. This means that as the wavelength decreases, the energy of the wave increases and vice versa. This relationship is described by the equation: energy = Planck's constant x frequency.

4. How is wavelength measured?

Wavelength can be measured in various units, such as meters, nanometers, or angstroms. It can be measured using instruments such as a spectrometer or by using diffraction techniques. In some cases, the wavelength of an electromagnetic wave can also be calculated using its frequency and the speed of light.

5. What is the significance of wavelength?

The wavelength of an electromagnetic wave is important because it determines the properties and behavior of the wave. It can affect factors such as the color of light, the type of energy carried by the wave, and its interactions with matter. Wavelength also plays a crucial role in various technologies such as telecommunications, astronomy, and medical imaging.

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