# Tag Info

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The Electrostatic Potential Energy we talk about is an energy stored in Electrostatic Field. Field is a reality and it has momentum, energy etc. stored in it. How to imagine it ? Consider that some space has a field in it. Then that space has stored energy in it in the form of field present, such that if you change the configuration of the charges creating ...

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Your calculation is nice, and the answer seems correct. Another way (less nice) to calculate it is to imagine the charge in the center as a small charged ball (to avoid infinities) and calculate by how much is the field energy lower when it is in the center than when it is far away. Due to symmetry and the Gauss law, the electric field in the former case is ...

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The force on the conductor must be zero. We will solve the problem in two steps. First, we will write down the external force $d\mathbf{F}$ on each infinitessimal charge $dq$ in terms of the external field $\mathbf{E}_{ext}$ and then we will integrate $d\mathbf{F}$ to get the total force. Note we need only consider the external force (i.e., the force from ...

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I don't think it is that tough to analyse. If a conductor is present in a uniform electric field then there will be redistribution of charges to counter Electric Field inside the conductor (so that the net field inside the conductor is zero). However in uniform electric field this redistribution of charges will not cause any net force on the conductor. Why? ...

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Yes, applying an electric field does create a pH gradient and in fact you can observe this simply by adding a suitable indicator to your system. For example see the section Demonstration of pH Gradient Formation in this article.

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If the wire is flexible, you could change its bounded area $A$, thus changing the magnetic flux. I'm imagining a "closed" loop where the two ends of the wire meet up. In your case of case of a uniform field that's perpendicular to plane of the wire, $\Phi_B=\pm BA$, depending on your choice for the direction of the corresponding area vector. Then, if you ...

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The solution for the plate capacitor is an approximation for separations much smaller than the plate area scale. Therefore it will be unusable if the distance between the plates becomes large. One thing the approximation does not take into account is that even if the distance between the plates goes to infinity or one plate is removed, one plate will still ...

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Faraday's law of induction can be written as $$\oint\limits_C \vec{E}\text{ }d\vec{l} = - \frac{d}{dt}\int\limits_A \vec{B}\text{ }d\vec{A}$$ where $C$ is some closed curve and $A$ is the area bounded by it. Recalling that the electric field is the gradient of the electric potential (i.e. something like a derivative) and that voltage is nothing but a ...

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Actually, cell phones do work in Faraday cages these days. What happens is that the conductor in the cage is not ideal, and there is some amount of leakage of electromagnetic radiation to and from the inside of the cage, specially at high frequencies. In order for the cage to be perfectly blocking it would need to have no holes at all (hence it is no longer ...

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The answer is heavily dependent on the material. For most materials the electric constant $\epsilon$ is very far from being a simple scaling factor, it has a complicated frequency response so that we write $\vec{D}(\omega) = \epsilon(\omega) \vec{E}(\omega)$ (assuming an isotropic and local medium, so that $\epsilon$ is scalar and local). For example, the ...

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The "center-of-charge" is part of a more general concept that is used quite often in physics: Multipole expansion. The general idea of multipole expansion is the following: If you view a charge (or mass) distribution from a large distance, then most of its internal structure is irrelevant to you. Instead, it suffices to do all calculations based on a few, ...

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I first show that we can write $$\Phi_j=\sum_{k=1}^NP_{jk}Q_k\tag{1}$$ for a given configuration of conductors; then it it will be straightforward to deduce $$Q_i = \sum_j k_{ij}V_j$$. To prove $(1)$ we draw on two concepts: principle of superposition, and the uniqueness of the solutions of electrostatics problems. Consider $N$ isolated conductors. ...

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I think that "because of linearity" should be read as "because of the superposition principle" (which does rely on the linear response of the dielectrics). You do not need to go into the detail of the field distribution: As in your example, set all potentials to 0, except for $V_i$. Denote this situation by $(i)$. The corresponding charges on each ...

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Mass and charge are not so similar for the charge having "center of charge". The notion of "center of mass" appears in many applications when number of bodies move. In this situation, the movement can be splitted into movement of center of mass and individual movements of bodies relative to the center of mass. This occurs because of dual role of mass: it ...

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The way I have heard it explained is not by the container but the water drops themselves. Statistically there is no way you can get a perfectly neutral water drop every single time. Eventually you will get a drop with a charge of 0.000000001 Farads. This tiny imbalance is enough to set the experiment in motion into a positive feedback system. You can think ...

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Of course you can define such a quantity, but the question is: does it mean anything physically? Contrary to what has been stated in some of the answers/comments, this quantity is not comparable to a "normalized" dipole moment. A dipole is a system of two charges equal in magnitude but opposite in sign. The corresponding dipole moment, which is of great ...

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I'll combine the comments into a guiding answer with some extra details here and there. An empty space containing a single point particle with charge $q$ is defined by two properties: The system's charge distribution $\rho(\vec{r})$ is zero everywhere except at the location $\vec{r}_0$ of the point particle. The integral over the entire space of the ...

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The Landau Pole is not a problem for QED because at scales much smaller than it (the Planck scale, which is smaller than the Landau pole by 260 orders of magnitude) the (negative) gravitational self-energy of the particle will more than cancel out its electromagnetic self-energy. So string theory is not necessary in this case, just gravity.

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Assume the contrary,suppose a point exists such that the local charge density is positive,say point A. Now from Gauss' law the total charge on the inner surface is negative.So there must exist a point B at which the local charge density is negative(otherwise the net charge will be positive). Now consider the field line from point A.It will originate from ...

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What is the electrical potential difference and why we have to talk about a difference and not about the electrical potential itself? Mathematically, the reason is that the force is proportional the gradient of a (not the) potential function. $$\vec F = -\nabla \phi$$ Note that a potential that differs by an additive constant $$\phi' = \phi + C$$ ...

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I have a guess, although I don't know if it is correct. If you model the globe as a simple insulating circular glass shell with a constant spatial charge density embedded in the glass in the immediate vicinity of the finger and solve Maxwell's equations numerically for the potential, you observe something like this: The rationale for placing a nontrivial ...

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This is true, however the bending is not much until one comes closer to the edge so it is usually neglected or too small to depict. Here's what I get when I simulate the system: This is the same system as a vector plot:

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No, glass and indeed all amorphous materials do not exhibit piezoelectricity because piezoelectricity is intimately connected to the crystal structure of the material. Roughly speaking, if the charges within the unit cell are asymetrically distributed then when the crystal is mechanically deformed the positive and negative charges may be displaced by ...

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The issue is that for a piezoelectric material you need a common orientation of the dipole moments. In normal glass there is no preferred direction and therefore an electric field will not create a bulk change in length. On the other hand it is possible to manufacture a piezoelectric glass, e.g. from a compound related to Strontiumtitanate (link to journal ...

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