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Veritasium "How Electricity Actually Works"

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hamster_nz:

--- Quote from: SandyCox on May 13, 2022, 08:21:04 am ---You cannot add inductors and diodes or DC-to-DC converters. The problem is about connecting two capacitors in parallel without any other components.

How do you think energy is transferred through a capacitor? Let's take a parallel plate capacitor with vacuum between the plates.

What about the airgap of a transformer?

--- End quote ---

Electrodacus already knows that, from message #169 when a DC-DC convertor was originally suggested:


--- Quote from: hamster_nz on May 04, 2022, 04:05:30 am ---It is also 'cheating'. I too could get any answer I want if I am free to add to the system. If I said "let me put an inductor in there, a diode, a switch and a trained imp that can push the switch really quickly" would you not agree that that is not the same problem any more?

--- End quote ---

Even knowing that Electrodacus went there, and put the diode, an inductor, a switch, and even the trained imp to push it.  :-//

SandyCox:
The problem is that circuit theory doesn't take the physical dimensions and the electrodynamic behavior of the system into account. That is why we get a contradiction.

Let's look at the more realistic example of using two lossless coaxial cables as "capacitors".

Let's see if Electrodacus' modern outlook on electronics can derive the equations that govern this example.

abebarker:
Is it possible to have an electric field without an associated particle? Is it possible to have an electric field without a charged particle?

I'm sure there are situations where it is much easier to calculate considering only the fields. I guess it is important to remember that numbers can be used to roughly describe reality and roughly predict things but they are not reality itself. It would be preposterous to think otherwise, absolutely posterior backwards. However, it does seem more common than not for people to think that words make reality rather than reality dictating the words (the little angels, little to no connection to reality).

vad:

--- Quote from: abebarker on May 13, 2022, 12:15:21 pm ---Is it possible to have an electric field without an associated particle? Is it possible to have an electric field without a charged particle?

--- End quote ---
Absolutely. Changing magnetic field creates electric field (Faraday’s law).

And you don’t need charged particles to have a magnetic field. For example, neutron has magnetic dipole moment. Magnetars are neutron stars that create strongest magnetic fields in the Universe.

timenutgoblin:
The pathological nature of the Two Capacitor Paradox problem leads to the observation that only the Law of Conservation of Charge is satisfied, but the Law of Conservation of Energy is violated.

https://en.m.wikipedia.org/wiki/Charge_conservation

According to the Wikipedia entry, half of the energy is 'lost' in the initially-charged capacitor after the switch is closed as shown in the mathematical expression below:

\$W_i = \frac{1}{2}CV_i\$

\$W_f = \frac{1}{2}CV_f^2 + \frac{1}{2}CV_f^2 = CV_f^2 = C(\frac{V_i}{2})^2 = \frac{1}{4}CV_i^2 = \frac{1}{2}W_i\$

Source: en.m.wikipedia.org/wiki/Two_capacitor_paradox

In order to satisfy Kirchhoff's Voltage Law after the switch is closed, both capacitors must have equal voltage. In this case, it is half the initial voltage of the initially-charged capacitor. Also, when the initially-discharged capacitor is connected after the switch is closed, this has the effect of doubling the total capacitance. If Q = CV and total capacitance doubles, then the voltage must be halved (V = Q/C) assuming charge is conserved. It then follows that if voltage is energy per unit charge, and charge is conserved after the switch is closed, then the initial energy must be halved if voltage is halved (across both capacitors). If the Law of Conservation of Charge is satisfied after the switch is closed, half of the initial energy must be lost to satisfy Kirchhoff's Voltage Law.

https://en.m.wikipedia.org/wiki/Voltage

Using the swimming pool analogy, assume that a swimming pool is filled with water and the floor of the swimming pool has a surface area of A (metres squared) and a height of h (metres). The weight and the height of the water is analogous to the charge and the voltage of the capacitor. If weight of the water can be expressed as F = mg then the gravitational potential energy of the water can be expressed as E = mgh.

https://en.m.wikipedia.org/wiki/Gravitational_energy

If the area of the floor of the swimming pool is increased from A to 2A (analogous to adding the initially-discharged capacitor) then the height of the water (analogous to the voltage across the capacitors) must be halved from h to h/2. The gravitational potential energy of the water (analogous to the electrical potential energy of the capacitors) must be halved, too. The weight of the water (analogous to the charge on the capacitors) does not change when the floor area (analogous to the total capacitance) is doubled.

Elaborating further with the swimming pool analogy, if the surface area of the floor is increased to the point where all of the water molecules are in direct contact with the floor then the effective height of the water would be the height of a single water molecule. The effective height of the water in the swimming pool would be approaching zero metres. The gravitational potential energy would be approaching zero, too.



I found a YouTube video showing the magnetic field of a toroidal transformer. You can see that the field exists only within the windings of the electromagnet. It's as though there are discrete magnets stacked with north to south poles arranged in a loop. What if the electromagnet was replaced with batteries connected in a loop with the positive terminal of one battery connecting to the negative terminal of the next battery? Would the electric field only be within the batteries or would it also extend/exist outside of the batteries?

Toroidal Electromagnet video: https://youtu.be/0-KaSGlDQ-8

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