# Why doesn't light affect a compass?

In our daily life a lot of photons of visible light, infrared and radio etc move around us. We know that light is an electromagnetic radiation. So why doesn't that electromagnetic radiation affect a magnetic compass?

• 'cuz the compass needle can't wiggle back-and-forth very far at the rate of 500 trillion wiggles per second. – robert bristow-johnson Mar 30 '15 at 16:00
• @robertbristow-johnson Good succinct answer, except that you should really use the correct SI prefix: terawiggles. – Reinstate Monica -- notmaynard Mar 30 '15 at 19:54
• I don't think @robert is right, though. A compass needle would be many millions of wavelengths long, so the magnetic field varies in direction over the length of the needle. I.e. we'd be observing many megatwitches along its length. – MSalters Mar 31 '15 at 8:32
• @robertbristow-johnson: Sure about that? 6 centimeter / 600 nm is 6E-2 / 6E-7 = 1E+5. We in fact may be down to kilotwitches. – MSalters Mar 31 '15 at 14:58
• Technically, light does cause (bits of) the needle (mostly, the electrons) to wiggle at around 400-800 THz, which is why we can see it in the first place. If it didn't interact with visible light at all, it would be totally transparent. – Ilmari Karonen Apr 1 '15 at 9:31

Most electromagnetic radiation is of very high frequency - the magnetic field changes many times per second. This means that the compass just doesn't have time to "follow" the magnetic field changes.

The only thing that does affect a compass is a DC magnetic field - usually this is a large piece of iron etc. that gets magnetized (e.g. by the earth's magnetic field) and thus causes distortion; or it can be a DC current loop of some kind.

But even the low frequencies of the mains (50 or 60 Hz depending on where you live) are much too fast to affect the compass (although in the presence of a strong source of electromagnetism, such as a large transformer, you can see vibration in the needle as observed by @vsz). Radio starts in the kHz (for long wave) to MHz (FM) or GHz (WiFi etc). And light, with wavelengths around 500 nm and a speed of 3x10$^8$ m/s, has frequencies in the hundreds of THz range. Too fast.

UPDATE - adding a bit of math(s):

A compass in the earth's field can be thought of as a damped oscillator: on the one hand there's the torque on the needle that is proportional to the displacement from magnetic North, on the other there's the inertia of the needle; and finally, there are damping terms (a good compass is critically damped - meaning that the damping is such that it will go to the right position in the shortest time). We can write the equation of motion as

$$I\ddot\theta + \mu\dot\theta + k\theta = 0$$

In this expression, $\mu$ is the damping term (proportional to the angular velocity) and $k$ is the factor that describes how much torque the needle experiences with displacement.

This is a general equation for a Simple Harmonic Oscillator (SHO), and we typically recognize three regimes: lightly damped, heavily damped, and critically damped.

How such an oscillator responds when you give it a displacement and then let it go depends on the kind of damping - see this graph:

In particular, the critically damped oscillator converges to its equilibrium position as fast as possible - which is why it's preferable for things like a compass.

Now when you drive a SHO with an oscillating force, you get a response that depends on the frequency of the drive signal and the natural frequency of the system. If you drive at the natural frequency, you get resonance and the amplitude becomes large; as the difference in frequency gets larger, the amplitude of the response gets smaller. For a lightly damped (or underdamped) system*, the amplitude response is given by

$$A = \frac{s_0}{\sqrt{\left[1-\left(\frac{\omega_d}{\omega_0}\right)^2\right]^2 +\left[\frac{\omega_d/\omega_0}{Q}\right]^2}}$$

In the limit of large frequencies, the response scales with

$$A \propto \left(\frac{\omega_0}{\omega_d}\right)^2$$

where $\omega_0$ is the natural frequency $\sqrt{\frac{k}{I}}$ and $\omega_d$ is the driving frequency. When the driving frequency is many orders of magnitude larger than the natural frequency, the amplitude response will be negligible.

As was pointed out in a comment by MSalters, at extremely high frequencies (above 10 GHz) the wavelength of the EM radiation becomes short compared to the length of the compass needle, so the above is further complicated by the fact that different parts of the needle will experience forces in different directions. All of which points in the same direction: the needle won't move.

* I am taking the easy way out here... did not find the expression for the critically damped driven oscillator and don't have the intestinal fortitude to derive it right now and trust myself to get it right. But this is 'directionally correct' even for critically damped oscillator

• But atleast the compass can follow the previous magnetic field even if its not able to follow the next magnetic field change so that should cause a distortion in the compass? – Bhavesh Mar 30 '15 at 16:45
• No - the EM field goes back and forth with a mean value of zero. The compass needle therefore has no bias in the presence of an EM field unless nonlinear effects came into play. Think of this as a critically damped simple harmonic oscillator driven at a frequency WAY above $\omega_0=\sqrt{k/m}$. There will be no offset. – Floris Mar 30 '15 at 16:52
• 50 Hz can affect a compass, especially if not shielded enough. I have an old 3A, 230V to 16V AC transformer, and when I turn it on, it produces a noticeable magnetic field. – vsz Mar 30 '15 at 20:46
• @BlueRaja-DannyPflughoeft - that might prove to be hard - or interesting. If you are filming at 29.97 Hz (one of the standard frame rates for HD) and have a 60 Hz transformer, you will probably see a nice slow motion of the needle... If you're running at 50Hz, you might try filming at 24 fps for something of a slowdown. – Floris Mar 30 '15 at 21:58
• @jpmc26 - thanks for the suggestion. I didn't ask you, but I did find a spot for it. :-) – Floris Apr 1 '15 at 1:06

The frequency is one very good argument (and I guess the most important factor) but it might be worth also looking at the magnitudes of the fields.

The earth's magnetic field has a strength of roughly $31µT$. The intensity of the sunlight hitting the earth is about $1300W/m^2$. Since the intensity is related to the electric field $E$ of an electromagnetic wave in the following way $$I=\frac{1}{2}\epsilon_0 c E^2$$ and the magnetic field strength is given by $B=1/c \times E$, one can easily calculate that the magnitude of the magnetic field is given by $$B\approx 3.3 µT.$$ So the earth's magnetic field is roughly ten times stronger. But: It can now be argued that fields with higher intensity would have greater impact. Now the frequency argument rescues us and in fact this argument seems to be the correct one, as one does not notice a deflection of a compass needle in the presence of a strong laser.

• I like that you took a look at quantifying this other aspect. – Floris Mar 30 '15 at 17:00
• Sunlight is not coherent. This means that field generated by it is not a single wave. The net effect of the incoherent photons will be orders of magnitude lower than that given. If instead a laser were being used, I guess the calculation is valid. – Keith Mar 31 '15 at 2:16
• @Keith, thank you for your input! Can you provide a source so that I can add this information to my initial post? – Merlin1896 Mar 31 '15 at 9:20
• Wouldn't "sunlight is white, which is because it consists of many different frequences" be enough of a source for "Sunlight is not coherent"? – Guntram Blohm supports Monica Apr 1 '15 at 11:46
• Sure, I was more aiming for a quantitative analysis of this fact. Especially the "orders of magnitudes lower" part should be underlined by a calculation or a good source, imho. – Merlin1896 Apr 1 '15 at 15:19

Basically the same reason as what Floris said, but this also has another important aspect:

Visible light has a far too small wavelength to affect a compass. Not only does the field oscillate too quickly around an average of zero – even at any single “snapshot” in time of the electromagnetic wave, there would nowhere be a large region where the field points in one direction. Only fractions of a micrometer are exposed to a field in a single direction; move a hair-width and the field may point in the opposite direction. Overall, at any given time, the forces on all parts of the needle cancel almost completely. So even if the light frequency wasn't to high for the needle to follow, it would still not move.

• If the frequency were lower, the wavelength would be higher ... so I think your last sentence depends on the width of the magnetic component of the compass and the inertia and friction the needle experiences. – Elliot Gorokhovsky Apr 2 '15 at 4:11
• @RenéG: I didn't mean “for lower-frequency EM radiation, the needle would still not move” (that would not be light anymore), I meant “if light happened to have a lower frequency, while all other properties were the same as in reality, i.e. the wavelength would still be to small to affect the needle as a whole” – hypothetically. Of course this would entail meddling with the values of the speed of light and the Planck constant... – leftaroundabout Apr 2 '15 at 8:50