Total Power Radiated

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

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PassThePi	Total Power Radiated Tweet 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)3770.001^2*(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)3770.001^2(10000) = 1.885mV PradTotal = (int(0\|2pi))(int(0\|pi))(Prad(theta,phi,r)r²sin(theta)dthetadphi PradTotal = 2pi0.132(-cos(\0\|pi)) = 0.528pi