[Physics] Why does a remote car key work when held to your head/body

electromagnetic-radiationeveryday-lifefrequencywavelength

I was trying to unlock my car with a keyfob, but I was out of range. A friend of mine said that I have to hold the transmitter next to my head. It worked, so I tried the following later that day:

  • Walked away from the car until I was out of range
  • Put key next to my head (it worked)
  • Put key on my chest (it worked)
  • Put key on my leg (didn't work)

So first I thought it has to do with height of the transmitter. But I am out of range if I use the key at the same height as my head but not right next to my head. Same applies when my key is at the same height as my chest. So it has nothing to do with height (as it appears).

Then I thought, my body is acting like an antenna, but how is that possible if I am holding the key? Why would it only amplify the signal if I hold it against my head and not if I simply hold it into my hand?

Here's a vid of Top Gear demonstrating it.

Best Answer

This is a really interesting question. It turns out that your body is reasonably conductive (think salt water, more on that in the answer to this question), and that it can couple to RF sources capacitively. Referring to the Wikipedia article on keyless entry systems; they typically operate at an RF frequency of $315\text{ MHz}$, the wavelength of which is about $1\text{ m}$. Effective antennas (ignoring fractal antennas) typically have a length of $\frac{\lambda}{2}=\frac{1}{2}\text{m}\approx1.5\text{ ft}$.

So, the effect is probably caused by one or more of the cavities in your body (maybe your head or chest cavity) acting as a resonance chamber for the RF signal from your wireless remote. For another example of how a resonance chamber can amplify waves think about the hollow area below the strings of a guitar. Without the hollow cavity the sound from the guitar would be almost imperceptible.

Edit: As elucidated in the comments, a cavity doesn't necessarily need to be an empty space; just a bounded area which partially reflects electromagnetic waves at the boundaries. The area occupied by your brain satisfies these conditions.

Edit 2: As pointed out in the comments, a string instrument is significantly louder with just a sounding board behind the strings, so my analogy, though true, is a bit misleading.

Edit 3: As promised in the comments, I made some more careful measurements of the effect in question, using a number of different orientations of remote position and pointing. I've posted these as a separate answer to this question.

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