Presented by Physics opens tax sapling learning Suppose the maximum safe average

Question

Presented by Physics opens tax sapling learning Suppose the maximum safe average intensity of microwaves for human exposure is taken to be 2.00 WIm If a radar unit leaks 10.0 W of microwaves (other than those sent by its antenna) uniformly in all directions, how far away must you be to be exposed to an average intensity considered to be safe? Assume that the power spreads uniformly over the area of a sphere with no complications from absorption or reflection. Number What is the maximum electric field strength at this distance? Number Note: early radar units leaked more than modern ones do. This caused identifiable health problems, such as cataracts, for people who worked near them.

Explanation / Answer

Solution:

Since the surface area of the sphere of radius r is given by

S = 4*pi*r^2,

the intensity of microwaves at distance r is

I(r) = P/S = P/(4*pi*r^2)

It is given that I(r) must be equal I, for human to be safe

I = P/(4*pi*r^2)

Therefore

r = (P/(4*pi*I))^(0.5)

By putting the values

r = (10/(4*pi*2)) = 0.63078313 m

The total energy density at this distance is I/C .At the same time it can be expressed through the electric field

strength E

(epsilon) * E^2

Therefore

I/C = (epsilon)*E^2

So,

E = (I/c*(epsilon))^(0.5)

E = (2/(8.85*10^-12*3*10^8))^(0.5)

E = 27.44623232 V/m

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