Glad you found it useful! You might enjoy looking at pictures of corona emission from power lines, which really let you see how strong the fields next to power lines are. The fields get so strong that they just rip electrons off of atoms, and you can see the glow as they combine back together. Wikipedia has some nice pictures here.

Yeah, OP is actually correct that it's the field. If you have say a 700 kV power line, that means the voltage difference between the two lines is 700 kV. The laws of E&M mean that there has to be an electric field between the two lines, so if you took a charged particle from one line to the other, it would pick up a ton of energy. Incidentally, this is why working on high voltage lines is kind of intense, and the lines themselves have to be incredibly smooth (I think surface imperfections are micron scale or smaller to avoid coronal emission). It's the electric current moving through the field, both of which are provided by the generating station, which carry the energy. It's easy to forget that Maxwell's equations still apply to transmission lines, but they do!

To answer what I think is OP's question, classical magnetic fields don't do any work because the force is always perpendicular to the direction of motion, so the Earth's magnetic field doesn't do anything for power transmission. The Earth doesn't have a large scale electric field, because ions in the atmosphere would rapidly adjust to cancel it out. There aren't a lot of ions in the lower atmosphere (and again, transmission lines are very carefully designed to not create new ones), so the electric field doesn't get cancelled out and we can send power down the lines.

The way modern encryption works is that the receiver has a private key (say two very large numbers) and they send out a public key (say the product of those two numbers). You can encrypt the message with the public key, but to decrypt it you need the private key. This works because it's trivial to multiply two large numbers together, but it's enormously expensive to factor the product of two large primes (until quantum computers come into their own).

If Alice wants to send a message to Bob, Bob can send her his public key. Alice can then encrypt whatever she wants to say to Bob and send it back. Alice may have to send her message through lots of people, but they can't read it without Bob's private key. This is end-to-end encryption - nobody along the way can read it.

Of course, maybe facetergram is sitting between Alice and Bob, and the message goes through them. Facetergram may say "hey, use my public key", then Alice sends a message to facetergram, then facetergram decrypts it, then re-encrypts it with Bob's public key and sends it off. In this world, Alice doesn't need to know Bob's key (convenient!), but facetergram can now read Alice's message if they want to. This is not end-to-end, since the message gets read in the middle.

Incidentally, this is why I think a lot of the law enforcement efforts are colossally stupid. If I'm a criminal, I'll just call up Bob and say "hey, Bob, what's your public key?" Then nobody in the middle can read the message. The software to do this isn't hard - I had to do it for a single homework assignment as an undergraduate. Letting facetergram decrypt your messages is an enormous security hole (what happens if they get hacked?), but if I'm a criminal I'd send messages in a way that they couldn't read. So, only legitimate users (or really dumb criminals) can have their messages read, at the price of potentially disastrous leaks.

This article lays out some of the reasons why we think there might be one. Also, we've seen unification happen in the past. First, electricity was linked to magnetism by Oersted when he noticed that an electric current made a compass move (I believe he actually noticed this during an in-class demonstration). Until then, there was no reason to think that static electricity had anything to do with compass needles pointing north. Then, EM was united with the weak force at high energy back in the 70's. There are indications (more details in the article) that there are some strange coincidences in various values for strong, weak, and EM strengths/gauge groups that hint at the three forces becoming one at energies 10^15 times the mass of the proton.

An imperfect but perhaps useful analogy is the Higgs boson. Even though it had never been seen, a lot of stuff made a lot more sense if the Higgs existed, which is why we spent billions of dollars building the LHC, and indeed the Higgs was there.

I know it's not true in general, that's why I said it's an oversimplification. Given we're explaining vector calculus to a five year old, though, I thought it would be OK. What is true, though, is that if a vector field only has a single component then the curl does have to be perpendicular to the field. That's what's going on with linearly polarized light, and why I didn't feel too bad about oversimplifying.

They aren't, unless you're talking about an electromagnetic wave in vacuum. For the case of a wave, the magnetic field comes from the changing electric field, and the electric field comes from the changing magnetic field. Maxwell's equations tell us then that the curl of E looks like the changing magnetic field, and the curl of B looks like the changing electric field. To (over)simplify the math, the curl of a thing is perpendicular to the thing, so that's why the magnetic and electric fields are perpendicular in a wave.

I don't think it's the weight. Gas only has about 30% more energy per pound than coal. The big difference is that coal takes a long time to burn - you can't floor a coal-powered engine like you can a gasoline one.

Incidentally this is also one of many reasons while coal-fired electrical plants are going away. Power plants increase/decrease their output all the time to match demand. It's really easy to do this with natural gas, but really hard with coal.

Not in the sense we usually use the word medium. For sound, the air is there wether or not there's a sound wave. The ocean is there wether or not there's a wave. But for an EM wave, there's no background EM field in empty space (at least classically) unless there's a wave going through.

I would say it's really just one number (epsilon-naught). What we call a magnetic field is just the effects of special relativity once you start moving charges. The speed of light is a fundamental property of spacetime, so it shows up once you start making relativistic corrections to electric fields, but you knew that going in so I wouldn't call it a property of electricity & magnetism. Once you have e0 and you know about special relativity, then you know what u0 has to be.

And lots of metals do burn, even before melting. Magnesium burns intensely. This table lists a bunch more.

To a photon, there's no such thing as time. From its point of view, it would be instant. One way of thinking about this is that in special relativity, distances shrink by a factor of sqrt(1-v^2/c^2). That is zero for a photon where v equals c, so from the photon's point of view, the distance between the Earth and the Sun is zero.

More technically, "age" is a funny concept in relativity. Time is seen differently by different observers. You need to specify both where and when something happened (not just "Alice met Bob at the corner of Main and Elm, but Alice met Bob at the corner of Main and Elm at 4:30 on Friday). If you take two different events at different times and different places, different observers won't agree on how far apart they are or when they happened, but they will always agree on the difference between distance squared and time multiplied by the speed of light squared (dx^2-c^2 dt^2). Since a photon moves at the speed of light the distance it moves dx in a time dt is just speed times dt, or dx=cdt, so dx^2-c^2 dt^2=0. As far as the universe is concerned, the distance between a photon leaving the sun and that photon hitting the earth is exactly zero. In our frame, that means dx is 93 million miles and dt is 8 minutes, but to the photon dx=0 and dt=0. There's no "right" answer for the age of the photon, since every frame is valid, but if you ask the photon, you'll get zero.

A lens takes all the light rays coming from a certain direction and bends them so they all end up in the same place. In the case of your eye, they need to end up on the retina. When your pupil is larger, you have to bend the rays coming in at the edge more than the rays going through the center of your pupil. Terrible vision (usually) happens because the lens of your eye isn't bending the light rays by the right amount. Let's say your lens only bends them half as much as it should. Light going through the center of your pupil isn't affected because it they go straight through. Rays near the center get bent by the wrong amount, but because they weren't getting bent very much still end up in nearly where they should have. But rays that come through the edge of your pupil need to get bent by a lot, so when your lens isn't working right, they end up a long ways from where they should. That makes your vision fuzzy, because the light from say a single light bulb ends up spread all over your retina. If you block the outer parts of your pupil, though, those rays that ended up a longs ways off and made your vision fuzzy get blocked, so the light that does make it through ends up where it is supposed to.

The limiting case of this is, as people have mentioned, a pinhole camera. The pinhole doesn't bend the light at all, so what you end up with is a picture that has been smeared out by the size of the pinhole. The smaller the pinhole, the sharper (and fainter) the image. The eye is better than a pinhole because it's at least trying to focus, but it is the same basic idea.

Late to the party, but I'm still going strong with my 6S. A new screen or battery is around $20, and it's like having a new phone. If you watch the tutorials, it's not that bad to do the repair yourself. I've replaced both the screen and battery twice now.