You're right that DC (direct current) power transmission has some important advantages of AC (alternating current) power transmission. In alternating current power transmission, the current reverses directions many times per second and during each reversal there is very little power being transmitted. With its power surging up and down rhythmically, our AC power distribution system is wasting about half of its capacity. It's only using the full capacity of its transmission lines about half of each second. Direct current power, in contrast, doesn't reverse and can use the full capacity of the transmission lines all the time.
DC power also avoids the phase issues that make the AC power grid so complicated and fragile. It's not enough to ensure that all of the generators on the AC grid are producing the correct amounts of electrical power; those generators also have to be synchronized properly or power will flow between the generators instead of to the customers. Keeping the AC power grid running smoothly is a tour-de-force effort that keeps lots of people up at night worrying about the details. With DC power, there is no synchronization problem and each generating plant can concentrate on making sure that their generators are producing the correct amounts of power at the correct voltages.
Lastly, alternating currents tend to flow on the outsides of conductors due to a self-interaction between the alternating current and its own electromagnetic fields. For 60-cycle AC, this "skin effect" is about 1 cm for copper and aluminum wires. That means that as the radius of a transmission line increases beyond about 1 cm, its current capacity stops increasing in proportion to the cross section of the wire and begins increasing in proportion to the surface area of the wire. For very thick wires, the interior metal is wasted as far as power delivery is concerned. It's just added weight and cost. Since direct current has no skin effect, however, the entire conductor can be carry current and there is no wasted metal. That's a big plus for DC power distribution.
The great advantage of AC power transmission has always been that it can use transformers to convey power between electrical circuits. Transformers make it easy to move AC power from a medium-voltage generating circuit to an ultrahigh-voltage transmission line circuit to a medium-voltage city circuit to a low-voltage neighborhood circuit. DC power transmission can't use transformers directly because transformers need alternating currents to move power from circuit to circuit. But modern switching electronics has made it possible to convert electrical power from DC to AC and from AC to DC easily and efficiently. So it is now possible to move DC power between circuits by converting it temporarily into AC power, sending it through a transformer, and returning it to DC power. They can even use higher frequency AC currents and consequently smaller transformers to move that power between circuits. It's a big win on all ends. While I haven't followed the developments in this arena closely, I would not be surprised if DC power transmission started to take hold in the United State as we transition from fossil fuel power plants to renewable energy sources. Using those renewable sources effectively will require that we handle long distance transmission better than we do now and we'll have to develop lots of new transmission infrastructure. It might well be DC transmission.
While I'm sorry to hear that your dog isn't well, I doubt that electromagnetic fields are responsible for her infirmities. The fields from the telephone adapter are too weak to have any significant effect and 60-Hz electromagnetic fields don't appear to be dangerous even at considerably stronger levels.
To begin with, plug-in power adapters are designed to keep their electromagnetic fields relatively well contained. They're engineered that way not because of safety concerns but because their overall energy efficiencies would diminish if they accidentally conveyed power to their surroundings. Keeping their fields inside keeps their energy inside, where it belongs. Moreover, any electric and magnetic fields emerging from an adapter probably don't propagate as waves and instead fall off exponentially with distance. As a result, it should be fairly difficult to detect electric or magnetic fields more than a few inches from the adapter.
Even if the adapter did project significant electric and magnetic fields all the way to where your dog sleeps, it's still unlikely that they would cause any harm. For years, researchers have been looking for a correlation between high-voltage electric power lines and a variety of human illnesses, notably childhood cancers such as leukemia. As far as I know, no such correlation has ever been demonstrated. In all likelihood, if there are any risks to being near 60-Hz electric or magnetic fields, those risks aren't large enough to be easily recognized.
In contrast to power adapters, cell phones deliberate emit electric and magnetic fields in order to communicate with distant receivers on cell phone towers. Those fields are woven together to form electromagnetic waves that propagate long distances and definitely don't vanish inches from a cell phone. Any electromagnetic hazard due to a power adapter pales in comparison to the same for cell phones.
Furthermore, cell phone operate at much higher frequencies than the alternating current power line. A typical cell phone frequency is approximately 1 GHz (1,000,000,000 Hz), while ordinary alternating current electric power operates at 60 Hz (50 Hz in Europe). Higher frequencies carry more energy per quanta or "photon" and are presumably more dangerous. But even though cell phones are held right against heads and radiate microwaves directly into brain tissue, they still doen't appear to be significantly dangerous. As unfond as I am of cell phones, I can't condemn them because of any proven radiation hazard. Their biggest danger appears to be driving with them; I don't understand why they haven't been banned from the hands of drivers.
Lastly, there are no obvious physical mechanisms whereby weak to moderate electric and magnetic fields at 60-Hz would cause damage to human or canine tissue. We're essentially non-magnetic, so magnetic fields have almost no effect on us. And electric fields just push charges around in us but that alone doesn't cause any obvious trouble. Research continues into the safety of electromagnetic fields at all frequencies, but this low-frequency stuff (power lines and cell phones) doesn't seem to be unsafe.
The electric circuit that powers your lamp extends only as far as a nearby transformer. That transformer is located somewhere near your house, probably as a cylindrical object on a telephone pole down the street or as a green box on a side lawn a few houses away.
A transformer conveys electric power from one electric circuit to another. It performs this feat using several electromagnetic effects associated with changing electric currents—changes present in the alternating current of our power grid. In this case, the transformer is moving power from a high-voltage neighborhood circuit to a low-voltage household circuit.
For safety, household electric power uses relatively low voltages, typically 120 volt in the US. But to deliver significant amounts of power at such low voltages, you need large currents. It's analogous to delivering hydraulic power at low pressures; low pressures are nice and safe, but you need large amounts of hydraulic fluid to carry much power. There is a problem, however, with sending low voltage electric power long distances: it's inefficient because wires waste power as heat in proportion to the square of the electric current they carry. Using our analogy again, sending hydraulic power long distances as a large flow of hydraulic fluid at low pressure is wasteful; the fluid will rub against the pipes and waste power as heat.
To send electric power long distances, you do better to use high voltages and small currents (think high pressure and small flows of hydraulic fluid). That requires being careful with the wires because high voltages are dangerous, but it is exactly how electric power travels cross-country in the power grid: very high voltages on transmission lines that are safely out of reach.
Finally, to move power from the long-distance high-voltage transmission wires to the short-distance low-voltage household wires, they use transformers. The long-distance circuit that carries power to your neighborhood closes on one side of the transformer and the short-distance circuit that carries power to your lamp closes on the other side of the transformer. No electric charges pass between those two circuits; they are electrically insulated from one another inside the transformer. The electric charges that are flowing through your lamp go round and round that little local circuit, shuttling from the transformer to your lamp and back again.
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