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

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

Step-by-step explanation:

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

`I = (\dot W)/((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\,(W)/(m^(2))`, then the radius is:

`r^(3) = (\dot W)/((4\pi)/(3)\cdot I )`

`r = \sqrt[3]{(3\cdot \dot W)/(4\pi\cdot I) }`

`r = \sqrt[3]{(3\cdot (10\,W))/(4\pi\cdot \left(1\,(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.