If the waves in an MRI can go through our body, why is it that light with its magnetic fields gets stopped at our skin?

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In an MRI, there are two fields being applied. One is a purely magnetic DC field, with an intensity of something like 1 T. The other is a radio-frequency pulse. The RF pulse is an electromagnetic wave, so it contains both electric and magnetic fields. The frequency of the RF pulse has to be at the correct resonance for protons in the magnetic field that's been applied. If the DC magnetic field is 1 T, then the RF pulse has to be about 40 MHz.

The DC field penetrates the human body because human flesh doesn't have strong magnetic properties such as magnetic permeability.

What about the RF pulse? The human body is mainly composed of salt water. The ions from the salt make it a relatively good conductor. When an electromagnetic wave enters matter that is a fairly good conductor, the electric fields in the wave produce oscillating electric currents. These currents then produce heating, just like any current flowing through a resistive medium. The heat energy has to come from somewhere; it comes out of the energy of the wave, and the wave is attenuated exponentially. The strength of the wave falls off exponentially with depth, the characteristic length of the exponential (called the skin depth) being $\delta\approx\sqrt{\rho/\pi\mu_o f}$, where $\rho$ is the resisitivity. Typical human body tissue has a resistivity of about 1 $\Omega\cdot\text{m}$. Plugging in numbers, we get a skin depth for an MRI pulse of about 0.1 m, which is enough to penetrate pretty deep into a human body without losing too much energy.

If the waves in an MRI can go through our body, why is it that light with its magnetic fields gets stopped at our skin?

The frequency of sunlight is about $10^{15}$ Hz. This much higher frequency gives a much smaller skin depth.

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In a word: it is not the magnetic field that is "stopped" by the skin, it is the electric field. Atoms and molecules of our body contain electrically charged electrons, and these electrons oscillate in the electric field of light, and take energy from it.

The outcomes may be different, depending on the frequency of wave, and on the particular substance. The most general outcomes are:

• Too slow waves (radio waves) take very large bodies to take a noticeable part of energy from them. Otherwise they "flow around" the body.

• Too frequent waves (X rays and gamma rays) are too fast for electrons to be swinged largely, and thus they keep their energy too - they pass through the body.

• Middle frequencies (that is, from infrared to ultraviolet) are either reflected back (by metals) or absorbed (by most other substances). Transparency can also be the case, but it is less often, and tend to appear in chemically simple substances (most crystals are such). Also, transparency is not absolute, it depends on frequency, and for any substance there could be transparency "windows" on the scale of frequencies (or wavelengths). Molecules of our skin are rather complex, but our bodies contain different water solutions which are transparent, and some other more or less transparent parts.

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