Question

At some instant and location the electric field associated with an electromagnetic wave in vacuum has the strength 87.5 V/m. Find the magnetic field strength (T), the energy density (J/m3), and the power flow per unit area (W/m2), all at the same instant and location.

Answer 1

a)
Given E = 87.5 V/m
E = Bc, where B is the magnetic field strength and c is the velocity of light.
B = E/c
= 87.5 / (2.9979 x 10⁸)
= 29.19 x 10^-8 T

b)
For the electric field, energy density, We = 1/2 oE²
= 1/2 x 8.85 x 10^-12 x (87.5)²
= 3.3879 x 10^-8 J/m³

For the magnetic field, energy density, Wm = [1/2o] x B2
= 1/ [2 x 4 x 10^-7] x [29.19 x 10^-8]²
= 3.3879 x 10^-8 J/m³

Total energy density = We + Wm
= 2 x (3.3879 x 10^-8 J/m³)
6.776 x 10^-8 J/m³

c)
Power per unit area, S = 1/o x EB
= [1/(4 x 10^-7)] x [87.5 x (29.19 x 10^-8)]
= 20.32 W/m².