A typical cell phone, which transmits microwaves, can have an output power as hi

Question

A typical cell phone, which transmits microwaves, can have an output power as high as 2.0 W.
(a) Approximating the cell phone as a point source that radiates evenly in all directions, calculate the radiation intensity of a cell phone at a distance of 2.00 in. which is the approximate distance from your cell phone to your brain. Convert inches to whatever metric units you need, and give your answer in milliwatts/cm2.
(b) The U.S. Food and Drug Administration limits the radiation leakage of microwave ovens to no more than 5.0 mW/cm2 at a distance of 2.00 in. How does your answer above compare with the maximum allowable power density leaking from a microwave oven? (Answer as the ratio of cellphone power / microwave power.)
(a) Approximating the cell phone as a point source that radiates evenly in all directions, calculate the radiation intensity of a cell phone at a distance of 2.00 in. which is the approximate distance from your cell phone to your brain. Convert inches to whatever metric units you need, and give your answer in milliwatts/cm2.
(b) The U.S. Food and Drug Administration limits the radiation leakage of microwave ovens to no more than 5.0 mW/cm2 at a distance of 2.00 in. How does your answer above compare with the maximum allowable power density leaking from a microwave oven? (Answer as the ratio of cellphone power / microwave power.)

Explanation / Answer

The radiation intensity of a cell phone at a distance is            I = P /(4pr^2)         Here P = 2.0 W           r = 2(0.0254 m)       I = (2.0 W)/(4p(2(0.0254m))^2)        = (61.67 W/m2)(1 mW/10^-3W)( 1m^2/10^-4cm2)        = 61.67 x 10^7 mW/cm2 --------------------------------------------------------------- b) Given that intensity I = 5.0 mW/cm2 = 50.0 W/m2 distance r = 2.00 in = 2(0.0254 m) Power P = I (4pr^2)               = (50.0 W/m2)(4p(2(0.0254 m))^2)               = 1.6214639 W The ratio of cellphone power / microwave power is          = ( 2.0 W)/(1.6214639 W)          = 1.2334533

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