Question

At some instant and location, the electric field associated with an electromagnetic wave in vacuum has the strength 90.5 90.5 V/m. Find the magnetic field strength, the energy density, and the power flow per unit area, all at the same instant and location.

Answer 1

Answer with Explanation:

We are given that

Electric field,E=90.5V/m

We have to find the magnetic field strength,the energy density and the power flower per unit area.

Magnetic field strength=$B=\frac{E}{c}$

Where $c=3\times 10^8 m/s$

Using the formula

$B=\frac{90.5}{3\times 10^8}=30.17\times 10^{-8} T$

Energy per unit volume,$u=\frac{1}{2}\epsilon_0 E^2+\frac{1}{2}\epsilon_0 B^2c^2$

Where $\epsilon_0=8.85\times 10^{-12}$

Using the formula

$u=\frac{1}{2}\times 8.85\times 10^{-12}\times (90.5)^2+\frac{1}{2}\times 8.85\times 10^{-12}(30.17\times 10^{-8})^2(3\times 10^8)^2$

$u=7.25\times 10^{-8}J/m^3$

Power flow per unit area=$S=\frac{BE}{\mu_0}$

Where $\mu_0=4\pi\times 10^{-7}$

$S=\frac{90.5\time 30.17\times 10^{-8}}{4\pi\times 10^{-7}}=21.7W/m^2$