Answer to Question #291391 in Physics for SelMel

Question

The most powerful 5G antennas work with a power of 120W. Assume that the human head is a sphere with a radius of 10 cm and that the human body is made of water. For simplicity, you can also assume that the antenna transmits radio waves in all directions evenly.

a) Estimate the upper limit (worst case scenario) of how much energy is captured by the human head if we are standing just below the antenna (5 m from the antenna). Indicate which laws and concepts you used in the calculation.

b) Estimate how long it would take to stand under the antenna to warm the brain by 0.1 ° C if all cooling modes are neglected.

c) List and describe as many ways as possible in which the human brain dissipates heat to the environment.

Answer 1

(a) Assume the power is decreasing by the inverse-square law:

$$P_H=P_o/r^2=4.8\text { W}.$$

(b) Apply thermal balance equations:

$$m=\dfrac43\pi r^3\rho,\\\space\\ Q=P_Ht=cm\Delta t,\\\space\\cm\Delta t=P_Ht,\\\space\\ t=\dfrac{4\pi\rho cr^3}{3P_H}=1\text{ h 1 min}.$$

(c) By convection and radiation, as well as by thermal conductivity.