what is difference between RADIATION INTENSITY power density

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what is difference between RADIATION INTENSITY power density?



Balanis Antenna Theory:

2.4 RADIATION INTENSITY
Radiation intensity ina givendirectionis defined as “the power radiated from an
antenna per unit solid angle.” The radiation intensity is a far-field parameter, and
it can be obtained by simply multiplying the radiation density by the square of the
distance.

Power density relates to the power received at a certain point, so it says something of the strength of the field at the location of the receiver. In your formula, W is in W/m2. The sun's radiation arrives at our earth at about 1 kW/m2.

The radiation intensity says something about the source.

You may know, the radian is just the length along a circle with radius =1. Therefore there are 2*pi radians in one revolution. radians are one dimensional, steradians are two dimensional.

Solid angle is the surface projected at a sphere with radius = 1m. As the area of a sphere with radius = 1m is 4*pi m2, there are 4*pi sr in a fully illuminated sphere.
When a source illuminates a surface of 1 m2 at 10m distance, the source illuminates a solid angle of 1/(4*pi*10^2) = 800e-6 sr.

When you have an isotropical emitter that radiates 10W, the radiation intensity is 10/(4pi) = 0.8W/sr. 0.8W/sr equals 0.8W/m2 at 1m from the source (assuming point source conditions).

When that same emitter only illuminates 10% of the full sphere, the radiation intensity is 10 times higher (so 8W/sr).

Power flux density [W/m2] = Radiation intensity [W/sr] / (distance [m] )^2.