# What is the strength of the magnetic field required to penetrate an average human body?

Introduction

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.

THE QUESTION

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.

• is this a homework-and-excercises question – Ilja May 1 '16 at 16:37

I do some work with magnetic fields in tissue as well for wireless power applications, though we don't typically deal with fields that strong hopefully I can help.

First of all human tissue is largely magnetically transparent at low frequencies. While modeling the electromagnetic properties of tissue is very difficult problem (this is why you largely see complex simulations in this field, instead of clean analytic solutions), most of these problems occur near RF frequencies. Its not until the >1 MHz range that we (my group in particular) tend to consider tissue a lossy barrier for magnetic fields. So for a 120 Hz magnetic field (a relatively low frequency), I believe you could treat the human body more or less as an air core.

The next task would be to find the field strength given by the solenoid. This can be approximated with:

$B = (\mu N I) / L$

Where B is the magnetic field, $N$ is the number of turns, $\mu$ is the magnetic permeability of the core, $I$ is the current in the solenoid, and $L$ is the length of the solenoid. Again for $\mu$ I suggest using the permeability of free space would be a fine approximation.

For your example, let's say L = 10 ft, $\mu$ = 4pi*10^-7 (T*m)/amp, B = 200 mT, N = 100 (I filled in for N). This would require a current of 4.8 kA at 120 Hz.

• Nice answer but wow that is insanely large current!! There aren't many commercially available systems that would produce that. – M Barbosa Jun 15 '16 at 23:11
• Better just to leave it that $NI \sim 5\times 10^5$ A. – Rob Jeffries Nov 16 '16 at 17:06