Question

At some instant and location the electric field associated with an electromagnetic wave in vacuum has the strength 96.5 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:

B = 32.17 x 10^-8 Tesla

u = 8.24 x 10^-8 J/m^3

P/A = 24.72 W/m^2

Explanation:

E = 96.5 V/m

velocity of light, c = 3 x 10^8 m/s

Let B be the magnetic field.

The relation between the electric field strength and the magnetic field strength is given by

B = E / c = 96.5 / (3 x 10^8) = 32.17 x 10^-8 Tesla

Let u be the energy density.

$u = \frac{1}{2}\times \varepsilon _{0}E^{2}+\frac{1}{2\mu _{0}}B^{2}$

$u = \frac{1}{2}\times 8.854\times 10^{-12}\times 96.5\times 96.5+\frac{1}{2\times 4\times 3.14\times 10^{-7}}\times 32.17^{2}\times 10^{-16}$

u = 8.24 x 10^-8 J/m^3

Let Power flow per unit area is

P/A = u x c = 8.24 x 10^-8 x 3 x 10^8 = 24.72 W/m^2