A high power cell phone tower radiates microwave power at a level of P=50W. The

Question

A high power cell phone tower radiates microwave power at a level of P=50W. The towers arrays are directional (not isotropic) and provide a gain G, of 17dB. So the effective power is P*G. (Note convert the dB factor to a ratio: Pout / Pin , before using this formula).

Calculate the Intensity ( in units of W/m^2 ) on the surface of a sphere of radius 100m. ( The radiation is not isotropic, but the gain factor makes up for this).

Calculate the electric field ( V/m^-1) at this distance from the tower assuming a medium of refractive index n= 1.33 (water). Hence find the voltage induced across a brain sized object of around 25cm.

Explanation / Answer

P=50W. The towers arrays are directional (not isotropic) and provide a gain G, of 17dB

17 dB as ratio==20log(P1/P2)

P1/P2=7/07=Pout / Pin

Pout=50*7.07=353.97 w

Intensity=353.97 w/(4pi*r^2)=2.81*10^-3 W/m^2

Hence find the voltage induced across a brain sized object of around 25cm.

v=integral E.d=2.81*10^-3 W/m^2

Formula for Conversion from Power Density (W/m2) to Electric Field Intensity (V/m)

V/m = (W/m2 x 377)1/2

V/m =sqrt(2.81*10^-3 W/m^2*377)=1.02 V/m

The voltage induced=E.d=1.02*0.25=0.257 v

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