Question

Suppose the maximum safe intensity of microwaves for human exposure is taken to be 1.00 W/m2 . (a) 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 intensity considered to be safe

Answer 1

Answer:

We must be approximately at least 1.337 meters away to be exposed to an intensity considered to be safe.

Explanation:

Let suppose that intensity is distributed uniformly in a spherical configuration. By dimensional analysis, we get that intensity is defined by:

$I = \frac{\dot W}{\frac{4\pi}{3}\cdot r^{3}}$ (1)

Where:

$I$ - Intensity, measured in watts per square meter.

$r$ - Radius, measured in meters.

If we know that $\dot W = 10\,W$ and $I = 1\,\frac{W}{m^{2}}$, then the radius is:

$r^{3} = \frac{\dot W}{\frac{4\pi}{3}\cdot I }$

$r = \sqrt[3]{\frac{3\cdot \dot W}{4\pi\cdot I} }$

$r = \sqrt[3]{\frac{3\cdot (10\,W)}{4\pi\cdot \left(1\,\frac{W}{m^{2}} \right)} }$

$r \approx 1.337\,m$

We must be approximately at least 1.337 meters away to be exposed to an intensity considered to be safe.