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I left a fork in my microwave and there were no sparks but there is now a small hole on the inside wall. The microwave works fine but is there anything dangerous about this?

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    Hello, and welcome to Stack Exchange. How big is the hole? Would you upload a picture of it? – Daniel Griscom Sep 19 '16 at 22:00
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    Is the hole just in the plastic? – Cascabel Sep 20 '16 at 2:48
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First off, what is the hole in? Is it just a hole in the plastic interior, or is a hole clean through the metal shielding? If you're confident it's just the plastic, that should be fine - that's not part of what's keeping it safe.

If it's actually a hole through the metal, then the power transmitted is roughly proportional to (d/λ)^4, that is, the fourth power of the ratio of diameter to wavelength. (See this question on physics, with more details found on another question there. That proportionality is from a simplified version of the problem, but it should be an okay approximation.)

With a 12.2cm microwave wavelength, using a 12.2cm hole as the baseline, 0.01% as much leaks through a 1.2cm hole, 0.1% through a 2.1cm hole, 1% through a 3.8cm hole, and 10% though a 6.7cm hole. And the full power of the microwave is 750-1500W, so the absolute worst case power leaked through those holes is .15W, 1.5W, 15W, and 150W. So for holes less than 1cm (leaking at most .15W) you should not have to worry. A 2cm hole (leaking at most 1.5W) also would likely be safe, since the energy shouldn't be too focused, but that's the range where I'd start getting nervous.

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The wavelength of the microwaves in the oven is roughly 12 centimeters or 4.7 inches. Therefore, for any of the microwaves to escape the interior of the oven, the hole would have to be 4.7 inches in diameter. If the hole is smaller than this, then the waves won’t leak. If the hole is larger, microwaves might leak. However, even if the waves leak out, it is highly unlikely that they will cause any damage, as microwaves are non-ionizing in nature and do not carry much energy as individual waves in open space. If they escape, the microwaves would dissipate (or die out) quickly in air, not causing any harm, and likely going unnoticed...

Source: Science ABC: What Happens if There’s a Hole in Your Microwave

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    If the holes are much smaller than the wavelength, it blocks transmission (so the tiny holes in the front screen do indeed make it safe), but I'm not sure there is a strict 12cm cutoff here. I would really like to see a better source than a popular science article (which itself doesn't cite any sources) to support this claim, and I went ahead and asked on physics. – Cascabel Sep 20 '16 at 2:47
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    "the microwaves would dissipate (or die out) quickly in air," - NOT. The same frequencies are used for communications (WIFI) over tens or hundreds of meters commonly, and what is limiting their range is the fact that very nondirectional transmission antennas are used, weakening the amount of power that hits an object OF EQUAL SIZE quickly with distance. The antenna characteristics of a random hole in a metal box can be far more unpredictable without doing serious maths. An oven would work badly if air absorbed (it would heat up a lot) or reflected (would be ineffective) them strongly. – rackandboneman Sep 20 '16 at 16:32
  • From the answer on that physics question, it looks like the transmitted power may be proportional to (diameter/wavelength)^4, which so while it will drop off below 12cm, it will still be leaking, e.g. at 10cm it'd leak half as much energy as at 12cm. That expression is from a very simplified model (plane waves on a flat surface with a hole) so a real microwave might leak more or less. But the bottom line is, the absolute assertion from the article you've quoted is incorrect. – Cascabel Sep 20 '16 at 16:38
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    Microwaves behave very similar to light, just that sometimes different materials are reflective/opaque/translucent/transparent to them (not always: Metal shields them, glass lets them through!). And the "resolution" is lower with a longer wavelength, that's why the holes in the metal grill inside the door are opaque to the microwaves. BTW, microwave ovens have 750 to 1500 watts, 1 watt of radiation (laser anyone?) can hurt you if it hits you the right way. – rackandboneman Sep 20 '16 at 16:40
  • @rackandboneman Microwaves ovens aren't lasers, they're not in phase or collimated or anything (in fact they're designed not to be), and light going through a hole smaller than the wavelength gets diffracted anyways so it really won't just be a beam. But the point stands - if hypothetically the leakage through a 12cm hole were the worst case, the full energy of the microwave, say 1000W, then a hole of about 2cm would still leak 1W, and I wouldn't be too excited about it. – Cascabel Sep 20 '16 at 16:44
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One thing that can also happen is that this setup will cause interference to radio communications (WIFI, HAM radio...) or even damage someone's radio. While not a direct threat of injury, if you interrupt somebody's business with interference from a known defective device, they can hold you liable for damages.

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