# Wavelength of an Electromagnetic wave

by rohanprabhu
Tags: electromagnetic, wave, wavelength
 P: 413 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?