Question

At some instant and location, the electric field associated with an electromagnetic wave in vacuum has the strength 70.5 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:

The magnetic field strength, the energy density, and the power flow per unit area are $2.35\times10^{-7}\ T$, $4.396\times10^{-8}\ J/m^3$ and 13.18 W/m².

Explanation:

Given that,

Electromagnetic wave strength E= 70.5 V/m

(I). We need to calculate the magnetic field strength

Using formula of Electromagnetic wave strength

$c= \dfrca{E}{B}$

$B=\dfrac{E}{c}$

$B=\dfrac{70.5 }{3\times10^{8}}$

$B=2.35\times10^{-7}\ T$

(II). We need to calculate the energy density

Using formula of energy density

$\mu_{total}=\mu_{E}+\mu_{B}$

$\mu_{total}=\dfrac{1}{2}\epsilon_{0}E^2+\dfrac{1}{2}\dfrac{B^2}{\mu_{0}}$

$\mu_{total}=\dfrac{1}{2}\times8.85\times10^{-12}\times(70.5)^2+\dfrac{1}{2}\times\dfrac{(2.35\times10^{-7})^2}{4\pi\times10^{-7}}$

$\mu_{total}=4.396\times10^{-8}\ J/m^3$

(III). We need to calculate the power flow per unit area

Using formula of poynting vector

$S=\dfrac{1}{\mu_{0}}EB$

Put the value into the formula

$S=\dfrac{1}{4\pi\times10^{-7}}\times70.5\times2.35\times10^{-7}$

$S=13.18\ W/m^2$

Hence, The magnetic field strength, the energy density, and the power flow per unit area are $2.35\times10^{-7}\ T$, $4.396\times10^{-8}\ J/m^3$ and 13.18 W/m².