Question

If a radar unit leaks 10.0 W of microwaves uniformly in all directions, how far away must you be to be exposed to an intensity considered safe (1.00 W/m²)?

a) 1.13 m
b) 2.25 m
c) 4.50 m
d) 9.00 m

Answer 1

To determine a safe distance from a radar unit emitting 10.0 W of power, the inverse square law is applied, yielding a distance of 1.78 meters to be exposed to an intensity of 1.00 W/m².

Step-by-step explanation:

To find out how far you must be from the radar unit to be exposed to a safe intensity of microwaves, which is 1.00 W/m², we use the inverse square law for intensities. This law indicates that the intensity (I) of an isotropically radiating point source is inversely proportional to the square of the distance (r) from the source. Therefore, I = P/(4π r²), where P is the power of the source. Given P = 10.0 W, we can solve for r when I is set to a safe level.

Using the equation I = P/(4π r²) and substituting the known values:

1.00 W/m² = 10.0 W / (4π r²)

1.00 W/m² * (4π r²) = 10.0 W

4π r² = 10.0 W / 1.00 W/m²

r² = 10.0 / (4π)

r = √(10.0 / (4π))

r ≈ 1.78 m. So, to be at a safe intensity, you must be approximately 1.78 meters away from the radar unit. This distance is not listed in the given answer options, indicating a possibility of a typo in the original question or answer choices.