Suppose you are an experimental nanobot researcher trial-ling a new form of medication that involves activation and control of nanobots within the cells of the interior of the human body by a magnetic field.
To control your nanobots, the field would have to be strong enough for the nanobots to detect from within the cells of the interior of the human body. In essence, it would need to have the following characteristics within the interior cells of a human body:
Frequency: 120 Hertz Amplitude: 200 miliTeslas uniform throughout the interior
You have on hand a long coil of insulated copper wire (coiled into a 10 feet long horizontal solenoid with a hollow diameter of 6 feet) to generate the required magnetic field.
You then wish to put a 6 feet tall, slightly obese human patient lying horizontally in the center of the hollow of the coil to begin his/her treatment.
However, you are aware that the tissues of the human body as well as the air in between the coil and the patient may block or reduce the magnetic fields generated by the coil such that the field in the interior of the human body may no longer be 120 Hz, 200 mT. In addition, the electrolytic qualities of the cells may modify the magnetic fields that do penetrate.
Given the characteristics above, What is the frequency and amplitude of the magnetic field that you would have to generate from the coil such that the field created in the interior of the human body after penetrating the human body will be uniformly 120Hz, 200 mT within the interior of the human body?
Note: You are allowed to make assumptions of the blocking and transductive potentials of the human body and air in your calculations as long as you justify them.