Cosmic microwave background radiation fills all space with an average energy density of 4 x 10^-14 j/m^3.(a) Find the rms value of electric field associated with this radiation.(b) How far from a 7.5 kW radio transmitter emitting uniformly in all direction would you find a comparable value?

Answer 1

There is a formula that relates radiation energy density to the E-field strength.

Get to know it.

Energy density = (1/2) epsilono * E^2

For an electromagnetic wave, there is an equal amount of energy in the magnetic field, as I recall.

For the E-field energy density at a distance R from that transmitter,
divide the radiated power by 4 pi R^2. That is the rate that energy is radiated away. Half of that power is due to the E-field. Divide by c for the E-field energy density. Set equal to the part (a) value and solve for R