Total Power Radiated by Isotropic Source: 1.885mV

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The total power radiated by an isotropic source in free space with an electric field strength of 1mV/m at a distance of 10km is calculated using the formula Prad(theta,phi,r) = (1/2)*eta*|E|^2. Substituting the values, the initial calculation yields 1.885mV, but there is skepticism about the simplicity of this result. To accurately determine the total power, integration over the entire surface area of the sphere at that distance is necessary. The integration process involves using spherical coordinates and results in a total power expression. Ultimately, the discussion highlights the need for careful consideration of the integration to obtain the correct total power radiated.
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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.
 
Last edited:
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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!
 
Last edited:
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
 
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