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

`1.9167* 10^(-7)\ T`

`2.9247498849* 10^(-8)\ J/m^3`

`8.7742496547\ W/m^2`

Step-by-step explanation:

`\epsilon_0` = Permittivity of free space =
`8.85* 10^(-12)\ F/m`

`\mu_0` = Vacuum permeability =
`4\pi * 10^(-7)\ H/m`

E = Electric field = 57.5 V/m

c = Speed of light =
`3* 10^8\ m/s`

Magnetic field is given by

`B=(E)/(c)\\\Rightarrow B=(57.5)/(3* 10^8)\\\Rightarrow B=1.9167* 10^(-7)\ T`

The magnetic field strength is
`1.9167* 10^(-7)\ T`

Energy density is given by

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

The energy density is
`2.9247498849* 10^(-8)\ J/m^3`

Power flow per unit area is given by

`(P)/(A)=uc\\\Rightarrow (P)/(A)=2.9247498849* 10^(-8)* 3* 10^8\\\Rightarrow (P)/(A)=8.7742496547\ W/m^2`

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