Question

At some instant and location, the electric field associated with an electromagnetic wave in vacuum has the strength 57.5 V/m. Find the magnetic field strength B , the total energy density u , and the power flow per unit area, all at the same instant and location.

Answer 1

Answer:

$1.9167\times 10^{-7}\ T$

$2.9247498849\times 10^{-8}\ J/m^3$

$8.7742496547\ W/m^2$

Explanation:

$\epsilon_0$ = Permittivity of free space = $8.85\times 10^{-12}\ F/m$

$\mu_0$ = Vacuum permeability = $4\pi \times 10^{-7}\ H/m$

E = Electric field = 57.5 V/m

c = Speed of light = $3\times 10^8\ m/s$

Magnetic field is given by

$B=\dfrac{E}{c}\\\Rightarrow B=\dfrac{57.5}{3\times 10^8}\\\Rightarrow B=1.9167\times 10^{-7}\ T$

The magnetic field strength is $1.9167\times 10^{-7}\ T$

Energy density is given by

$u=\dfrac{1}{2}\epsilon_0E^2+\dfrac{1}{2\mu_0}B^2\\\Rightarrow u=\dfrac{1}{2}\times 8.85\times 10^{-12}\times 57.5^2+\dfrac{1}{2\times 4\pi \times 10^{-7}}(1.9167\times 10^{-7})^2\\\Rightarrow u=2.9247498849\times 10^{-8}\ J/m^3$

The energy density is $2.9247498849\times 10^{-8}\ J/m^3$

Power flow per unit area is given by

$\dfrac{P}{A}=uc\\\Rightarrow \dfrac{P}{A}=2.9247498849\times 10^{-8}\times 3\times 10^8\\\Rightarrow \dfrac{P}{A}=8.7742496547\ W/m^2$

Power flow per unit area is $8.7742496547\ W/m^2$