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 50.0 W of microwaves (other than those sent by its antenna) uniformly in all directions, how far away (in cm) must you be to be exposed to an intensity considered to be safe

Answer 1

The safe distance is 199 cm approximately 200 cm

Step-by-step explanation:

Safe intensity = 1.00 W/m^2

wattage of radar leaked radar = 50.0 W

safe distance from the microwave will be = ?

We know that the intensity of a wave radiated uniformly in all direction is given as

`I` =
`(W)/(A)`

where

W is the wattage of the leaked radar

A is the radial area, which is the area of a sphere that encapsulates the region through which this wave spreads uniformly.

From the equation above,

`A` =
`(W)/(I)` = 50/1 = 50 m^2

But the area of this sphere
`A` =
`4\pi r^(2)`

where

r is the safe distance from the radar source

substituting for the area, we have

50 = 4 x 3.142 x
`r^(2)`

50 = 12.568
`r^(2)`

`r^(2)` = 50/12.568 = 3.978

r =
`√(3.978)` = 1.99 m = 199 cm ≅ 200 cm