Not by simplified equation. If modeling is required, which program would you recommend?
Vivien, "2 km" sounds like penetration of em radiation into earth, right?
If so, the soil is usually layered and even inside each layer inhomogeneous, and its electrical properties depend on the water content. So, calculating the field strength can be no more than a good guess, unless you know exactly all the details. Which frequency band are you interested in? I feel that in order to receive a measurable field strength at a depth of 2 km, it has to be an extremely low frequency.
you could buy an emf meter or use a hall sensor connected to an arduino program you write and upload to the usb powered device an atmel 328 nano arduino clone which will need the arduino die and drivers for that board it is written in similar to c plus plus many of the same rules apply. a hall sensor is like a ditch that trips when next to or taken away from a magnetic field. if you built an array of six with different field strength ratings if that exists or the same thing made more or less sensitive with a resistor and calibrated also in software how the values are read you could build your own. I paid about thirty for my emf meter. those one inch ball magnets only give off a field an inch away but could destroy digital circuits. an electrified electromagnet would be much stronger. computer monitors give off a good amount within five inches. I work in a recording studio and this one computer monitor for the camera system was the only source of emf radiation I could find. speakers magnetically couple with other things like the power supply transformer in big screen tv's and the humming noise the refrigerator makes when it is cooling things and power boxes outside. my ionizer gives off the meter record and it's negative ions I haven't checked it with and without the fan. with inductors and proper grounding computers would not need fans that being said I looked at your question better. felix Bloch invented nuclear induction which is rf pumped on an inductor with nuclear material attached and is what led to magnetic resonance imaging technology. a polarized electromagnet working as an oscillating dipole hooked to a kind of radio receiver circuit which the inductor is part of. so hall sensor array might not get the diatance without an amplifier but a microphone and amplifier is a form of electromagnetic pickup but you would have to have a parallel soundtrack of the audible noises that happened to filter out. the MRI rf circuit idea might just require a nuclear diode if you need to build your own diode search up cats whisker diode that was an early thing that worked and they can be tested with most any multimeter. actual mrI equipment might be your best bet but it is dangerous you can get sucked into those. without actually inserting a wifi probe with sensor on a small tunneling robot that doesn't displace much material and can fit into something you might not get it back out and it could turn Into pollution and rust. or not be big enough to send the signal. you could try oil drilling equipment and a wire but I'm not sure unless you found a deep cave to get halfway there to set up an MRI machine I don't know if there would be a danger of drawing the earth core to where the machine is. a software defined radio would be a step to having your own MRI equipment and essential if you want to use software with it. go to discovercircuits.com and see if any rf circuits you want to incorporate into your custom MRI equipment and read felix Blochs nuclear induction paper and use his technique how MRI was invented.
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