# average energy density of electromagnetic wave formula

Clearly, the larger the strength of the electric and magnetic fields, the more work they can do and the greater the energy the electromagnetic wave carries. $\begin{array}{lll}I&=&\frac{{\mathrm{c\epsilon }}_{0}{E}_{0}^{2}}{2}\\ &=& \frac{\left(3.00\times {\text{10}}^{8}\text{m/s}\right)\left(8.85\times {\text{10}}^{\text{-12}}{\text{C}}^{2}\text{/N}\cdot {\text{m}}^{2}\right){\left(1\text{25 V/m}\right)}^{2}}{2}\\ & =& 20. Unless otherwise noted, LibreTexts content is licensed by CC BY-NC-SA 3.0. Q2: What are the examples of Electromagnetic Waves? (a) If a radar unit leaks 10.0 W of microwaves (other than those sent by its antenna) uniformly in all directions, how far away must you be to be exposed to an intensity considered to be safe? The velocity of the em wave in the dielectric is less than 3 $10^{8}$ m/s. Nowadays, this technology has revolutionized our life. the frequency wave is 5 × 1 0 1 4 H z . However, they do carry energy. Energy Density and the Poynting Vector Overview and Motivation: We saw in the last lecture that electromagnetic waves are one consequence of Maxwell's (M's) equations. To find E0, we can rearrange the first equation given above for Iave to give, [latex]\displaystyle{E}_0=\left(\frac{2I_{\text{ave}}}{c\epsilon_0}\right)^{1/2}\$/extract_itex], $\begin{array}{lll}E_0&=&\sqrt{\frac{2\left(8.33\times10^3\text{ W/m}^2\right)}{\left(3.00\times10^8\text{ m/s}\right)\left(8.85\times10^{-12}\text{ C}^2\text{/N }\cdot\text{ m}^2\right)}}\\\text{ }&=&2.51\times10^3\text{ V/m}\end{array}\\$. By extension, the power of a wave should probably be replaced with the more useful concept of its power density. However, there is energy in an electromagnetic wave itself, whether it is absorbed or not. These equations, along with the Lorentz force formula mathematically explain all the laws of electromagnetism. In fact, for a continuous sinusoidal electromagnetic wave, the average intensity Iave is given by, $\displaystyle{I}_{\text{ave}}=\frac{c\epsilon_0E_0^2}{2}\\$. power per unit area carried by an electromagnetic wave: (a) Assuming all of the radio waves that strike the ground are completely absorbed, and that there is no absorption by the atmosphere or other objects, what is the intensity 30.0 km away? . This caused identifiable health problems, such as cataracts, for people who worked near them. In a vacuum, the average electric energy density (u E) and average magnetic energy (u B) because of static electric field E and magnetic field (B) which remains constant with time and is given by u E = 1/2ε0\[E^{2}$ and u B = $B^{2}$/2μ0 Consider a plane electromagnetic wave propagating along the -axis. The electric field vectors (E) and the magnetic field vectors are vibrating along the Y, and the X-axis respectively, and the direction of propagation of a wave is shown on the Z-axis. It is the flux of energy which is critical to ocean waves. uE  = 1/2ε0Erm$s^{2}$ and  uB = Brm$s^{2}$/2μ0. One more expression for Iave in terms of both electric and magnetic field strengths is useful. So, from here, we understood that the waves produced in the string are the em waves and these em waves are transverse. There is an energy density associated with both the electric field E and the magnetic field B. It means the force because of the radiation pressure of visible light on the surface area of 10 cm2 is ( 7 10-6 ) x ( 10 10-4 )= 7 10-9N. (Hint: Half the power will be spread over the area of a hemisphere.) What is the intensity of an electromagnetic wave with a peak electric field strength of 125 V/m? We begin by deriving the energy flux in general conditions. Another way to prevent getting this page in the future is to use Privacy Pass. with the same form applying to the magnetic field wave in a plane perpendicular the electric field.