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33

Ohm's Law is not a construct which can be derived. It is essentially a generalized observation. It is only useful for a few materials (conductors and medium resistivity), and even then virtually all of those materials show deviations from the ideal, such as temperature coefficients and breakdown voltage limits. Rather, Ohm's Law is an idealization of the ...


23

You could start from Drude in zero magnetic field, that equates the derivative of the momentum $\vec p$ by the electrostatic force $\vec F_{el} = q \vec E$ as a product of charge $q$ and electric field $\vec E$ minus a scattering term (with time constant $\tau$; compared to Newtons second law that does not feature the latter, crystal term): $~~~~~~\dot ...


4

In the sea of electrons picture, the electrons in the conductor are not at rest: they are jiggling about like gas particles, colliding and changing direction constantly. You can think of them as billiard balls at zero gravity, confined in the volume of the piece of conductor at hand. According to thermal physics, their average kinetic energy is related to ...


3

According to Faraday's law of induction, $$\mathcal{E} = -N {{d\Phi} \over dt}$$ you will need a change in the magnetic flux $\Phi$ in order to get an EMF or an electric field. So if you just put your coil in the magnetic field of the permanent magnet, you will not measure a current. There will only be a current, if you move the coil around so that the flux ...


3

Basically, you want to find the proportionality between the total current and the voltage difference between cathode and anode. Let's assume that the current flow is radial under steady-state conditions, which basically allows me to ignore the $z$-direction throughout. In a steady-state solution, we will have $\nabla \cdot \vec{J} = 0$; moreover, if we ...


3

If you really mean "points", see the answer to this question. Basically, the logic is as follows: If you try to inject a finite current at a "point" in a bulk, it will necessarily lead to a divergent current density $\vec{J}$ in a neighborhood of that point, proportional to $r^{-2}$ (where $r$ is the distance from the injection point.) A divergent current ...


3

Since Michael has already pointed out that the problem as stated has no answer, I will answer a different question instead: if we have a resistive spherical shell with inner radius $a$, outer radius $b$, and bulk resistivity $\rho$, and the surfaces of this shell are coated with a conductive layer, what is the resistance between the inner and outer surface? ...


3

The ammeter measure the current flowing through itself. If you want to measure the current flowing through another component, then you must make the current through the ammeter equal to the current through the component. If you wire it in series, that's true. If you wired it in parallel, the current would be unevenly divided between the component and the ...


2

Related question on EE: Does perfect insulation exist? (especially the part about vacuum) Insulators and conductors The property of a material to carry charges from one point to another is what electric current is. The difference between insulators and conductors lies in the electron band structure they posses. In conductors the Fermi-level ...


2

Induction cooktops contain electromagnets below each pot or pan station. When a station is switched on, electric current flows through wire wrapped around an iron core. In order for magnetic flux to be induced in the iron core, the electric current must constantly change, so the current must alternate. The iron core concentrates the magnetic flux ...


2

In my opinion, the mathematical equation we call Ohm's Law is best taken not as a “law”, a fact about the universe, but as the definition of resistance. $$R \overset{\mathrm{def}}{=} \frac{V}{I}$$ Given this definition of the quantity $R$, we can then make (as other answers have mentioned) the empirical observation that many materials have approximately ...


2

There are two different $V$'s here. Suppose the power station outputs at 10,000 V. By the time the wire makes it to your house, this may have dropped to, say, 9,000 V. The $V$ in the first equation refers to the voltage difference you can use, which is 9,000 V (between the wire you receive and ground). The $V$ in the second equation refers to how much ...


2

The short answer This is not 100% true since it assumes DC transmission, but it gives the simplest form of the idea: even if the transmission lines are themselves at high voltages, that doesn't directly mean anything, since voltages are not defined relative to anything special (they're defined relative to some other line which is in parallel with your ...


2

You are feeling an electric current because the "live" wire of the electrical outlet is connected to the "ground" of your phone. The same effect can be felt in the US (or wherever "back home" is for you) with an improperly wired desk lamp - or one that has an unpolarized plug. The electric field induces a small current in you because your body has a ...


1

Clarification from another source: Source: Physics For Scientists And Engineers, Paul A. Tipler and Gene Mosca, Sixth Edition, W. H. Freeman and Company, New York, 2008, p. 971, Fig. 28-20. I maintain that the loop will act the same as the bar. In other words, if you cut a thin slit down the center of the bar and less than the length of the bar (you ...


1

I think this picture answers the question There battery's terminals are not charged. It's just a chemical reaction that starts the charge. There's a Zn and a CuSO4. When they meet each other via a cable, the Zn gives 2 electrons to ChSO4. Cu gets rid of SO4, leaves 2 extra electrons to SO4 and takes the 2 electrons it got from Zn. Then we have SO4 ...


1

If by our goal is to see the fields due to some charge or current, look at Jefimenko's equations. For electric fields electric field they can be caused by charge density, the rate of which charge density changes or by the rate that current density changes. For magnetic fields they can be caused by current or by the rate at which current changes. Since you ...


1

In a diode, or PN junction, you have two regions: region P with an excess of holes: the material is doped with atoms having 3 electrons instead of 4 region N with an excess of electron: the material is doped with atoms having 5 electrons instead of 4 Each two regions are neutral but when we place them side by side, some electrons and some holes diffuse ...


1

The electrons do not even enter the wire, because the redox reaction between the substances in each of the nodes never occurs. Once the wire is connected to each of the nodes, electricity will flow through as electrons will be more attracted to the node with the greater reduction potential.


1

To answer your question in one word, "Yes" Now, onto the explanation:- According to Faraday's Law, you will get a current in a conductor when the amount of magnetic flux linked with the conductor changes. Note that it is immaterial whether the source of the magnetic field is a permanent magnet or an electromagnet. All that needs to happen for you to ...


1

I disagree with the other two answers, or at least believe they are not very clear. The important point is that, as you suggested, a induction cooker only consumes significant amounts of energy when a pot is actually on top of it. There are, of course other losses, but without any metal object in the vicinity, the cooktop is like a transformer without a ...


1

Ohm's Law actually follows the definition of power, current and voltage. Let's begin by defining power $P$, current $I$ and voltage $U$ as $P = \displaystyle \lim_{\Delta t \to 0} \frac{E}{\Delta t}$, $I = \displaystyle \lim_{\Delta t \to 0} \frac{Q}{\Delta t}$ and $U = \frac{E}{Q}$. We then find for a constant current $I$ with a constant voltage $U$ that ...



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