Question

At microwave frequencies, the power density considered safe for human exposure is 1 (mW/cm²). A radar radiates a wave with an electric field amplitude E that decays with distance as E(R) = (4000/R) (V/m), where R is the distance in meters. What is the radius of the unsafe region?

Answer 1

The radius of the unsafe region is 100,000 meters, for a microwave frequencies, the power density considered safe for human exposure is 1 (mW/cm²). A radar radiates a wave with an electric field amplitude E that decays with distance as E(R) = (4000/R) (V/m), where R is the distance in meters.

Step-by-step explanation:

To find the radius of the unsafe region, we need to equate the power density of the radar wave to the safe power density. The power density is given by:

P = E2 / (2μ₀c)

Where E is the electric field amplitude and μ₀ is the permeability of free space.

Rearranging this equation, we get:

E = √(2Pμ₀c)

Substituting the given values, we have:

E = √(2(1 mW/cm²)(10⁻⁴W/m²) (4π x 10⁻⁷ Tm/A) x 3 x 10⁸ m/s)

E = 4 x 10⁻⁸ V/m

Now, we can solve for the distance R when the electric field amplitude is equal to the safe value:

4 x 10⁻⁸ V/m = (4000/R) V/m

Simplifying the equation, we find:

R = 10⁵ m

Therefore, the radius of the unsafe region is 100,000 meters.