Question

At some instant and location, the electric field associated with an electromagnetic wave in vacuum has the strength 69.5 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.

Magnetic Field=__________ T -Energy density=__________ J/m^3 -Power flow per unit are=________ W/m^2

Answer 1

A) 2.19*10^{-7} T

B) 4.27*10^{-8} J/m^3

C) 12.82 W/m^2

Step-by-step explanation:

The relation between magnetic and electric field is given by:

`c=(E)/(B)`

A) Hence, the magnitude of the magnetic field is:

`B=(E)/(c)=(65.9(V)/(m))/(3*10^(8)(m)/(s))=2.19*10^(-7)T`

B) the energy density is:

`u_E=(1)/(2)\epsilon_0 E^2=(1)/(2)(8.85*10^(-12)(C^2)/(Nm^2))(69.5(V)/(m))^2=4.27*10^(-8)(J)/(m^3)`

C) the flow per unit area can be computed with the magnitude of the Poynting vector:

`S=c\epsilon_0|E|^2=(3*10^8(m)/(s))(8.85*10^(-12)(C^2)/(Nm^2))|69.5(V)/(m)|^2=12.82(W)/(m^2)`

hope this helps!!