Total Power Radiated by Isotropic Source: 1.885mV

[PassThePi]

What is the total power radiated by an isotropic source in free space is |E| = 1mV/m at a distance of 10km?

Relevant Eqns:
Prad(theta,phi,r) = (1/2)*eta*|E|^2

Prad(theta,phi,r) = (1/2)*377*0.001^2*(10000) = 1.885mV

Is this correct? I feel like it can't be that simple.

 

[yungman]

Your 1mV/m is measured at a point 10Km away, to calculate the total power of the isotropic source( E is equal in magnitude at any point on the sphere), you need to have some sort of integration of the whole surface of radius of 10Km.

I don't understand your formula at all!

 

[PassThePi]

Oh I think I see...

Prad(theta,phi,r) = (1/2)*eta*|E|^2

Prad(theta,phi,r) = (1/2)*377*0.001^2*(10000) = 1.885mV

PradTotal = (int(0|2*pi))(int(0|pi))(Prad(theta,phi,r)*r²sin(theta)dtheta*dphi

PradTotal = 2*pi*0.132*(-cos(\0|pi)) = 0.528*pi