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# the power per square metre is 400µW/m2.

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At 100m from the antenna of a cellular base station in open country, measurements show that the power per square metre is 400µW/m2. What power per square metre could be expected at 200m from the base station? Show your working and explain any assumptions you make.

Mar 14, 2018

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Area of circle at 100m = pi r^2 = pi (100^2) = 10,000 pi m^2

Total power = 10,000pi m^2  *  400 microwatts/m^2 =  4 x 10^6  pi  microwatts

This total wattage will be distributed over a larger area at 200 m    Area = pi (200^2) 40,000 pi m^2

Total watts/area = (4 x 10^6 pi microwatts) /  (40,000 pi m^2) =  100 microwatts/m^2

I am not sure where you are in your studies, so I will edit this question assuming you are working on surface areas of SPHERES    (Answer is the same)

Surface area of a SPHERE =  4 pi r^2     =   4 pi (100^2) = 40,000 pi  m^2

40,000 pi m^2  *  400 microwattats/m^2 = 16 x 10^6 pi microwatts

at 200 m   area =  4 pi (200^2) = 160,000 pi m^2

( 16 x10^6 pi microwatts) / (160000 pi m^2) = 1 x 10^2 microwatts/m^2

Mar 14, 2018
edited by ElectricPavlov  Mar 14, 2018
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Thank you very much for your answer this has made it alot clearer. All it takes is someone to just explain it.

Thank you x

Guest Mar 14, 2018
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