New answers tagged electric-fields
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In what direction would current flow in the coil?
The magnetic field on and near the axis decreases as you move away from a coil. As the second coil moves away from the first coil the flux through it would decrease. By Lenz's, law, ...
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What is the meaning of $\vec H$ with respect to the total field?
Here the problem is that you are using too many notations and you are changing them constantly.
The master equation in electrostatics :
$$ \vec{D}= \epsilon_0 \vec{E} + \vec{P}.$$
(i) $ \vec{D} $ is ...
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Can Sagnac effect be observed in coiled, rotating electrical cables conducting electric signals?
My first thought was: yeah, you can have counterpropaging electic signals in a single cable, so I rather expected that in that type of setup a Sagnac effect can be elicited.
I have a point of concern ...
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Is Faraday's cage described in electrostatic 100% insulated?
Electrostatics problems do not consider cases where charges are moving. They are valid problems, but more complex. So you have one electrostatic problem. You add a charge and wait again for ...
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In an electrostatic field with zero divergence everywhere, where is the charge located?
You can look at the required charge when your field is given by your formula in a finite domain $D$ and zero outside. Physically, this gives you a surface charge on the boundary $\partial D$ given by:
...
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Why can't we calculate potential at a particular point due to an infinitely long thin wire with uniform positive linear charge density?
We can definitely calculate the electric potential, as long as we choose a valid (in this case, non-infinity) reference point with respect to which we measure the potential.
The common choice in ...
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How current is induced when there is a change in external magnetic field?
If still charges in a wire loop do not respond to a (or have their own) magnetic field,…
Electrons at rest (even in a wire loop) have their own magnetic field. Each electron is also a magnetic dipole....
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How current is induced when there is a change in external magnetic field?
It is actually not the changing magnetic field
$\mathbf{B}$ directly, which generates the current.
According to Faraday's law of induction
$$\nabla\times\mathbf{E} = -\frac{\partial\mathbf{B}}{\...
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How current is induced when there is a change in external magnetic field?
I'm not sure how to explain 'how', because Faraday's law of induction is a fundamental law of Physics, and asking 'how' is asking why there is such a law. There just is.
It's not actually current ...
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How do charge carriers "know" how much voltage to use for work in a specific component?
Once you accept circuit theory, then things must work as the theory describe. It is still a valid question to ask why is circuit theory true and why circuit theory is apparently non local.
Given there ...
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How do charge carriers "know" how much voltage to use for work in a specific component?
This is communicated to the current through surface charges on the surface of conductors and at the interface between conductors of different conductivities.
So, for example, consider a circuit ...
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How do charge carriers "know" how much voltage to use for work in a specific component?
Anthropomorphizing the physics in this case has made your problem far weirder than necessary. The fact that you have different resistances means there is different current flow for a given voltage. It ...
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Why don’t charge carriers constantly accelerate in an electric circuit?
So my question is: how come the charge carriers don’t accelerate
constantly? Is there some kind of balancing force that keeps them at a
constant drift velocity?
The charge carriers alternatively ...
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Explaining Faraday's Law With Lorentz Transformations of $E$ and $B$ Fields
Just a small detail, Faraday's law is about inducing electromotive forces (emf's), not currents. To make the link between current and emf, you'll need to go beyond Faraday's law and make some ...
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Why is there no negative sign in the linear form calculation of voltage but there is a negative in the integral form?
The minus is a reminder of the convention used in electrostatics. When $\nabla \times \vec{E}=0$, $\vec{E}$ is the gradient of a potential and by convention $\vec{E} = -\nabla \phi$. If $\gamma$ is ...
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Why is AC current attractive and DC repulsive?
Electric current (both AC and DC) has no attractive or repultive power. Nerves and muscles in the human body work on electrical current in the form of ion-transfer (because ions are charged particles),...
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Is the superconducting wire in a equilibrium DC circuit free of surface charge?
The claim that a superconducting wire should be free of surface charge is based on the unique properties of superconductors, particularly the behavior of the superconducting state.
In a ...
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How does an Electromagnetic Accelerator work?
This is not the Lorentz force, which describes electric and magnetic forces on electric charges, it is the force of a magnetic field on a magnetic dipole (here's the wiki page about it).
When the coil ...
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Which theory/model explains electrons movement inside a transmitting antenna?
You need to study “antenna theory”. In short the signal is high frequency so a lot of assumptions from dc/lumped element circuit models go out the door. You can model the antenna as a series of ...
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Which theory/model explains electrons movement inside a transmitting antenna?
Here is the part you are missing.
The high-frequency AC current in an antenna is changing so quickly that the current at the center of a dipole can be completely different from the current at the ...
- 90k
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Why electric potential can be evaluated by conservative electric field?
Electric potential definition refers to conservative part of total electric field. Sometimes sources neglect to mention this. So electric potential is always defined, even when total electric field is ...
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What is $E$ with respect to the relation between an electric field and its polarization density?
The $\mathbf{E}$ in the formula is the electric field at equilibrium $\mathbf{E}_\mathrm{total}$ (In the following answer I shall use $\mathbf{E}_\mathrm{total}$ in place of $\mathbf{E}_\mathrm{n}$).
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Exact Definition of electrostatic field
Static means something that does not change in time, that is
$$\frac{\partial \mathbf{E}}{\partial t}=0.$$
The Maxwell equations defining electric field are:
$$
\nabla \cdot \mathbf{E}=\frac{\rho}{\...
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Exact Definition of electrostatic field
You are correct, those conditions are not the same.
$\nabla \times \vec{E} = 0$ does not necessarily imply that the field is electrostatic. The well-known example is induced electric field of ideal ...
- 35.5k
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Exact Definition of electrostatic field
Does a time-independent charge distribution necessarily imply an electrostatic situation? . The electrostatic field is a field such that it is static ,ie, time invariant. This implies a time ...
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Why electric field is unaffected due to dielectric shell?
The fields of surface charges on the dielectric shell cancel. Think of the polarization in the dielectric shell as a charge $-q$ accumulated at radius $a$ and a charge $q$ accumulated at $b$. For ...
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Definition of electrostatic field
You are correct in that an electrostatic field is a field E(r) that does not depend on time. You seem to be confused by the definition
$$ -\nabla \phi(r) = E(r)$$
Maybe it would help to contrast this ...
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Why is AC current attractive and DC repulsive?
I think you may be referring to something like a person holding and unable to release an object they are grasping that becomes electrically live.
In electric shock parlance this is sometimes referred ...
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Increase of potential when charging a capacitor
So, both the electric fields of the capacitor and the battery point in
the same direction, thus adding up a higher electric field within the
capacitor.
The electric field in a parallel plate ...
- 68.8k
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Electromagnetic waves produced from a sinusoidal current
The current density is concentrated in the $z$-axis
$$\mathbf{J}(\mathbf{r},t)=I_0 \mathbf{e}_z \delta(x)\delta(y) \sin(\omega t)$$
where $\mathbf{e}_z$ is the unit vector in $z$ direction
and $\delta$...
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Increase of potential when charging a capacitor
Here is the circuit when current has ceased to flow with some extra annotations.
Let us take unit positive charge around the circuit $XY(Z)X$,
$X\to Y$ : Work done by external force is $\...
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Energy transfer with electromagnetic waves
In order to better understand what happens in case of lighting a bulb I suggest that you ask yourself the question how does the water know where to flow out if there is a hole in the bottom of a ...
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What is the intuitive reason why Ampere's law is incorrect?
The other answer already shows that Ampere's law and
charge conservation in their differential forms
$$\vec\nabla\times\vec{B}=\mu_0\vec{J}$$
$$-\frac{\partial \rho}{\partial t}=\vec{\nabla}\cdot\vec{...
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What is the intuitive reason why Ampere's law is incorrect?
It is a mathematical fact that the divergence of the curl of a vector field is always zero. I'm not sure whether one can give an "intuitive reason" for this or not, but it is in fact true.
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Unconvincing sentence in wikipedia
Ignore the word "static" in the first quote, or at least don't interpret it to mean "this only holds in the static case" in which all charges are stationary. The units of the ...
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Potentials of two near conductors
For a sphere charged with a total charge ( Q ), the potential at a point located at a distance ( r > R ) (where ( R ) is the sphere's radius) from the sphere's center is given by ( \frac{kQ}{r} ). ...
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A question about Coulomb's law for one moving and one stationary charge
Yes. In the frame of the stationary charge $Q$, the electric field is: $$\mathbf E_Q = \frac{kQ\mathbf r}{r^3}$$ The force at a (moving) test charge $q$ is $\mathbf F = q\mathbf E$.
But the inverse is ...
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In a conductor responding to an external $E$-field do the electron clouds just shift slightly or do the electrons fully dissociate to go to one side?
The density of free electrons in a metal is enormous compared to the charge imbalance induced by any field that won't destroy your laboratory. So, the "sea" of electrons in the metal is ...
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