Question

There exist various standards for the safety limits of human exposure to electromagnetic radiation. One of them is the IEEE standard, whose recommendations for the maximum permissible time-average intensity of the Poynting vector in uncontrolled environments (where individuals generally have no knowledge or control of their exposure to EM fields) at frequencies between 100 MHz and 300 GHz are as follows:

(i) Pavg.max = 2 W/m² for 100 MHz ≤ f < 300 MHz,
(ii) Pavg.max = f/150 W/MHz m² for 300 MHz ≤ f < 15 GHz,
(iii) and Pavg.max = 100 W/m² for 15 GHz ≤ f < 300 GHz. Based on this standard, compute the maximum permissible levels for the rms intensities of the electric and magnetic fields in air at frequencies of 150 MHz, 1.5 GHz, and 15 GHz, respectively.

Answer 1

The maximum permissible rms intensities for the electric and magnetic fields in air at frequencies of 150 MHz, 1.5 GHz, and 15 GHz are calculated using the IEEE standard guidelines and the relationship of intensity to the E and B fields.

Step-by-step explanation:

To solve the mathematical problem completely regarding the safety limits of human exposure to electromagnetic radiation, we will calculate the maximum permissible levels for the rms intensities of the electric (E) and magnetic (B) fields in air at specified frequencies according to the IEEE standard guidelines. The intensity (I) of an electromagnetic wave is related to the E and B fields as I = (E^2/Z0)/2, where Z0 is the characteristic impedance of free space (approximately 377 ohms).

• At 150 MHz, the Pavg.max is 2 W/m2. Using I = Pavg.max and the equation above, we can give a complete answer for E and B.
• At 1.5 GHz, Pavg.max is calculated with Pavg.max = (1.5 GHz)/150 W/MHz m2 = 10 W/m2. Again, we find E and B using the formula for intensity.
• At 15 GHz, Pavg.max is 100 W/m2, and we follow the same process as before to determine E and B.

Calculations:

1. For 150 MHz: E = sqrt(2 * I * Z0) = sqrt(2 * 2 W/m2 * 377 ohms) = 34.3 V/m. B = E / Z0 = 34.3 V/m / 377 ohms = 91.0 μT.
2. For 1.5 GHz: E = sqrt(2 * I * Z0) = sqrt(2 * 10 W/m2 * 377 ohms) = 77.2 V/m. B = E / Z0 = 77.2 V/m / 377 ohms = 204.8 μT.
3. For 15 GHz: E = sqrt(2 * I * Z0) = sqrt(2 * 100 W/m2 * 377 ohms) = 244.9 V/m. B = E / Z0 = 244.9 V/m / 377 ohms = 649.3 μT.