Question: During a battle between two extremely powerful space wizards, a beam of magical lightning has blasted a perfectly circular hole around 10 feet in diameter directly through an Earth-sized planet. In and out like a gunshot through paper. How would this impact life on the planet after this event, if at all?

NOTE: The incident occured about 150 miles south of the planet's north pole.

Answer: 
I would assume this depends on how the Beam did its work. If it just "deleted" the matter in its way, just about nothing would happen excpet that some random Animal will have a pretty bad day.

If the Beam melts its way across you may see a pretty big explosion on both sides of the Planet. The first when the Beam enters and the 2nd when it goes out. So overall, a bunch of Animals would have a bad day. But not much more.

If it pushes everything to the side, like a Force Field. Well then still not a lot would happen. Except someone in the distant future will see a strange long diamond bolt going from one side of the Planet to the other.
This is because at some point, or depth, the Beam pushes dense stuff into very dense stuff. Thus creating bling blings.

At the end of the day, 3 Meters just isnt that wide and the total amount of Energie blasted into the plant could be scrapt of as a Rounding Error.

For anything drastic to happen, you gonna need a wider beam. Making it more powerfull but keeping the diameter the same wouldnt do anything. Sure at some point the Impact spots would look like several nukes went down, but at some point it makes no difference anymore. You need to affect a bigger area at once.

Example, a Photon at Lightspeed dosnt hurt you. Even although it carries momentum. But let's say the Photon is 1 Meter across. Well then you are going to have a bad day.

The wider the beam is, the more stuff gets turned into dust and the bigger the Impact Explosion is.

Sorry for Misspellings , I am German.
Soil doesn't behave like that when hit. We have craters, not cylindrical cavities all the way through when a meteor falls for example. In order to displace so much matter neatly, the amount of energy involved would probably be enough to turn the planet into plasma.

[XKCD What If no. 20](https://what-if.xkcd.com/20/) is about how deep a 100-feet wide diamond meteor would penetrate the Earth. It has this quote:

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> Oddly, the speed that something is going doesn’t really affect how deeply it digs into the ground. Isaac Newton came up with a very clever idea for estimating how deeply projectiles will go in their targets before stopping. It turns out that no matter how fast a projectile is going, if it hits something that’s about the same density, it will only go about one body-length in.
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So for an object to go through the Earth, it would need to be either as dense as a stellar core, or it would need to have a mass comparable to the Earth's. Even [Mars-sized Theia, upon hitting Earth ~4 billion years ago didn't go all the way to the core of the Earth](https://en.wikipedia.org/wiki/Giant-impact_hypothesis). An energy weapon (either using lasers, or electricity as in the question) would have to provide a similar amount of energy to obtain the same effect.

Let's assume that instead of smashing through the planet like that, the magic beam teleports away all matter in its path. [This paragraph from L. Dutch's answer summarizes the result:](https://worldbuilding.stackexchange.com/a/185677/21222)

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> An end to end hole on Earth would not be stable, and would collapse under the gravitational force exerted by the planet. That would alone would release a large amount of energy which would surely evaporate the oceans if not even melt the crust.
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The hole would not be stable exactly because of what gave the Earth its round shape. [A prerequisite for a body to be a planet is for it to have enough self-gravity to overcome rigid body forces](https://en.wikipedia.org/wiki/Definition_of_planet#IAU_definition). In laysman terms, the magma/core material forming the walls of the hole won't be strong enough to keep the planet around it from collapsing into the hole. This collapse will dissipate vast amounts of energy.

I don't know how to calculate that energy, but I have an idea to approximate it. While the hole doesn't close, every point in the remaining Earth would have ~1.5m below it to fall onto. Of course they can't all fall 1.5m as they will crunch upon each other along the way, but the potential energy being turned into kinectic will be mostly the same.

That would be the equivalent to the mass of the Earth falling from a 3m height. So...

$$ mgh = (5.972 \times 10^{24}kg) \times (9.8m/s^2) \times (q.5m) = 8.8 \times 10^{25} j$$

Looking at [this handy table](https://en.wikipedia.org/wiki/Orders_of_magnitude_(energy)) tells us it's like the total energy output of the sun in half a second, or 50 times all the solar energy that Earth gets in one full year. It is also like being hit by the dinosaur killing asteroid five hundred times. You'll have that energy dissipated on the planet within a moment. That does not bode well to life.