The electric field created in a curvature energy sensor on air microparticles is used to obtain a temperature-humidity map by stereoradially of the sensor design to detect and measure the temperature and humidity of certain local region of the environment space. Likewise,considering the curvature energy as the deviation of any field interaction,even the obstruction to its proper flow, is designed and created a humidityresistor sensor to the control and optimization of humidity in a space with different gradients of humidity, pressure and temperature in a radial detection and measuring. Then the sensing problem is a problem of free boundary conditions where is satisfied an energy functional of norm ,to curvature functions that satisfy in the temperature and humidity function the change limit condition This carries to that the temperature-humidity sensor must be designed on a length gauge to measure the changes of humidity and temperature in the space.