Final answer:
To remain safe from the microwaves emitted by a radio transmitting antenna of a howitzer mounted radio, you need to be at least approximately 0.797 meters (or about 2.62 feet) away from the antenna.
Step-by-step explanation:
To determine the distance at which you need to be from a radio transmitting antenna of a howitzer mounted radio to remain safe, we can use the concept of radiant intensity. Radiant intensity is defined as the power per unit solid angle, and it is uniform in all directions from the antenna. Given that the transmitting antenna leaks 10.0 W of microwaves uniformly in all directions, we can calculate the distance at which the intensity is considered safe by setting the intensity equal to the maximum safe intensity.
We can use the formula:
Intensity = Power / (4πR2)
Rearranging the formula to solve for distance:
R = √(Power / (4πIntensity))
Replacing the values with Power = 10.0 W and Intensity = 1.00 W/m², we can calculate the distance:
R = √(10.0 / (4π × 1.00))
R ≈ 0.797 m
Therefore, you need to remain at least approximately 0.797 meters (or about 2.62 feet) away from the transmitting antenna to be safe from microwaves.