Questions tagged [electrostatics]

Electrostatics is concerned with the electrical fields and scalar potentials of stationary electrical charges and charge distributions. Use this for questions about electromagnetic situations in which currents and magnetic fields are absent, otherwise use the [electromagnetism] and/or [magnetic-fields] tags.

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Velocity between two opposing charges

My question is Q: when two charges $+ Q $ and $-Q$ symmetrically approach each other to $L$ length then what would be their individual and combined velocities?
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Multipole terms of Electrostatic energy

If we consider the Potential and electric field of a Dipole, could we infer that for a dipole : $V \propto 1/r^2$, $E \propto 1/r^3$ , $da \propto r^2$, then Electrostatic potential energy should ...
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Question about work and rectangle [closed]

See this question: "Two protons and two electrons are located at the corners of a rectangle with side lengths a and b. There are two essentially different arrangements. Consider the work required ...
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What is the electric field between two conducting parallel plate capacitors?

Actually i am confused about the difference b/w electric field due to a non-conducting charged plate and conducting charged plate. And what should we assume when it is not mentioned that which plate ...
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Find the The space density of the bound charges as a function of $\varepsilon$

Question: The gap between the plates of a parallel-plate capacitor is filled with isotropic dielectric whose permittivity $\varepsilon$ varies linearly from $\varepsilon_{1}$ to $\varepsilon_{2}\left(\...
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Sodium chloride crystal,

I am studying the potential electric of a sodium chloride crystal, where the actors says: To evaluate the potential energy we first observe that every positive ion is in a position equivalent to that ...
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1answer
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Charge piled up at the junction of two different materials

In this question, I am unable to understand why charge would pile up at the junction in the first place. This is current electricity, not electrostatics, and the current is same through both the ...
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1answer
54 views

Why effect of Coulomb's Force is same on more than two charges?

As we have developed the idea of Electric Field Lines from coulomb's law. If two equal and opposite charges are in plane all the effect of electric field vectors add to line joining the two points, ...
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How can we use the electrostatic boundary conditions in electromagnetic waves?

The boundary conditions for an electromagnetic wave passing from one linear dielectric media to the other (both having no free charges or current) are taken as: $$B_{\perp_1} -B_{\perp_2} =0$$ $${\...
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Microscopic explanation of the Joule effect and dielectric on capacitors

I understand intuitively that the resistor heats up when electrical energy travels through it and mathematically that the capacitor stores more charge when we fill the space between the conductive ...
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Metallic bonds get weaker during electrostatic induction?

If the cations are held together by the sea of electrons (metallic bonding), and if we apply electrostatic induction then what happens to the region of atoms that have a deficit of electrons? Are ...
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Expansion of Green's Function in Spherical Coordinates in Jackson

So I was reading about the expansion of the Green function in Spherical coordinates from Classical Electromagnetism by J.D. Jackson and I'm really confused about a subtle step that he makes to go from ...
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Full capacitance matrix symmetry property - how to derive it?

In this excellent article, the author, in sec. 1.4 describes the full capacitance matrix properties. He writes: The capacitance matrix is symmetric: $C_{ij} = C_{ji}$. This is related to the fact ...
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Curl of an Electrostatic Field

According to Maxwell's equations: $$ \vec{\nabla}\times\vec{E} = -\frac{\partial B}{\partial t}$$ But if we have an electric field that is dependent upon both the radial distance and angles, we can ...
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Why Coulomb's Law is only valid for point charges?

Why Coulomb's Law is only valid for point charges? Is there any reason? Why this law is not valid for other charges rather than point charges?
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Direct, brute force computation of electric field of homogenous sphere of charge [closed]

I'd like to find the electric field produced by a homogeneous sphere of charge density $\rho$. I know you can use Gauss's law to solve this problem in two seconds. And I know you can simplify the ...
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Dielectric constant or permitivity of copper

I'm trying to simulate a capacitor made of copper plates in comsol multiphysics. What is the value that I should use for the dielectric constant or permittivity of the copper plates? I've read that ...
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Is this a valid way to show an infinite sheet of charge has a uniform field using Gauss's law?

From a pre-academic studies book, the example uses a gaussian surface outside of the charged sheet to show that because the flux through it is 0, the field on both ends has to be equal. Is this a ...
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Why electric potential definition demand the positive sign of test charge?

Why does electric potential definition need to distinct a positive test charge since the result will be the same even with a negative test charge? We could define electric potential with agnostic sign ...
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Electrostatic induction - how to quantify it with a theoretic integral expression or like?

Assume that a certain distribution of charges $\rho$ generates an electrical field $E_{ext}$ in the surrounding space. We also note the corresponding generated potential $V_{ext}$. Assume furthermore ...
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On The Potentials Of Conservative Fields

I was working on some E&M problems when I came across one I did not quite understand, the problem goes something like this: The potential at a radial distance r from a point charge q is V=$\frac{q}...
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Source of the electric field in a loop falling through a constant magnetic field

Figure shows a loop falling down through a constant magnetic field which points into the screen. Due to the Lorentz Force a magnetic force is present on the top part of the wire which pushes the ...
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1answer
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Infinite Conducting Planes

I was reading about the method of image charges, where they've (Irodov) mentioned an "infinite conducting plane". Is this just like an infinite sheet, or does it cover one half of the space? ...
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Charge redistribution in term of Force

Suppose two spherical conductors each with a different radius. Initially, they are charged independently up to charge $Q_1$ and $Q_2$. Now let's that they are connected through a wire. Then the charge ...
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1answer
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What is the potential to the left of the conductor? [closed]

I’m trying to find the potential to the left of a grounded conducting wall if there is a charge q to the right of it. I was told that the potential isn’t necessarily zero since I have to take into ...
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Is magnetic dipole moment the same as electric dipole moment?

In the problem below, why does the second method used to calculate magnetic dipole moment $\vec {\mu}$ essentially use the definition of the electric dipole moment $\vec {p}$? Is magnetic dipole ...
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3answers
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Why the potential is not infinite?

One way to calculate potential (using infinity as our reference point) is to sum all the contributions of charges that are around. Let's say I want to calculate the potential at some point on charged ...
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Differential form of Gauss's law from Coulomb's law in spherical coordinates [duplicate]

Coulomb's law for the static electric field of a point charge is given by $$\overrightarrow{E}=\frac{1}{4\pi\epsilon_0}\frac{q}{r^2}\hat{r}$$ Now if we take the divergence of both sides of the above ...
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How much voltage do you need to force charge into a material?

If I'm using electricity not to induce steady-state current, but instead to force as much charge as possible into a given material, given I know the relevant properties of the material, how do I ...
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3answers
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Why capacitance is constant? [duplicate]

I am new to the field of electrodynamics and I recently came across the definition of capacitance as $$C = \frac{Q}{V}$$ It is said that capacitance is constant, which implies that total charge of the ...
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1answer
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Permissible Electrostatic Potential

Let us consider a $1D$ real function $V(x)$. When is this a classical electrostatic potential? My take on the problem: $V(x)$ must be differentiable everywhere. In fact, we should be able to ...
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High voltage anode electron gun

In the image it can be seen that the anode voltage of a SEM field emission electron gun is up to 30kV. I think that at that voltage an electric arc can occur between the electrons and the anode, or am ...
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Why does Air act as a conductor in presence of a Strong Electric Field

We know that Air is a good insulator but why does it become conducting in presence of a strong electric field?.
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About Rutherford scattering

I am trying to derive Rutherford's scattering formula, with the coordinate system and polar coordinates chosen as in the picture below. Angular momentum conservation yields $mvb = mr^2 \dot{\varphi}$....
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1answer
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Maximum Voltage Between Long Coaxial Cylinders

Derive an expression for the maximum voltage allowable between long coaxial cylinders of radii $R_1$,$R_2$ $(R_2> R_1)$, if the field strength in the insulation between them is not to exceed $E_m$....
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Where does half of the work done in charging a capacitor is dissipated? [duplicate]

The energy stored in a charged capacitor of capacitance $C$ with $V$ voltage across it is: $$U= \frac 12 CV^2$$ Whereas the work done in charging the capacitor is: $$W= CV^2$$ This means that $(1/2)CV^...
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Potential due to an insulating shell containing a hole (so that there is no charge in that area) at an arbitrary point inside the shell [closed]

There is an insulating shell (spherical, of radius $R$) which previously had a total charge $Q$, spread over the whole area, i.e. $A = 4πR^2$ Now a hole is being cut on the surface of area 't4πR^2'. I ...
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If the potential is continuous across a surface, why is the electric field discontinuous then?

Across a surface the potential is continuous so: $V_{\text {above }}=V_{\text {below. }}$ Taking the negative gradient both sides we have $-\nabla V_{\text {above }}=-\nabla V_{\text {below }}$ ,...
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Charge distribution conductor in electric field

Surface charge density of a conductor at a particular region on its surface is inversely proportional to the radius of curvature at that region. But this is valid only when there is no external ...
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Why is an electric dipole neutral overall and still has energy?

We are taught that only charged particles have an electric field in their vicinity and a neutral object does not. But a dipole is neutral overall and still produces an electric field. Why?
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Electric field inside a conductor is zero

My professor has stated that the electric field inside a conductor is 0.I understand this However, he has also said that even if the conductor has some hole in it, the electric field inside this hole ...
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Charge density of Conductor

Surface charge density of a conductor at a particular region on its surface is inversely proportional to the radius of curvature at that region. But this is valid only when there is no electric field. ...
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2answers
56 views

Why does Gauss's law apply to any shape of a closed surface?

What seems to incredibly bother me is why Gauss's law applies to any shape of a closed surface. Moreover, the fact that the electric flux is proportional to the enclosed charge is by many sources ...
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1answer
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Field in the case of two charged plates [duplicate]

A questions goes like this: X and Y are large,parallel conducting plates close to each other. Each face has an area A. X is given a charge Q. Y is without any charge. Points A, B and C are as shown ...
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Is principle of superposition valid for extended conducting objects whose charge distribution is affected by presence of other charges nearby?

let me explain my question with an example. Say we put a charge at the centre of an metallic hollow charged sphere and measure electric field at a distance larger than the radius. It is easy to ...
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Maxwell solution in differential forms

Maxwell equation's in differential form: $dE = 0 \ and\ \ (\ast d \ast)E = p$ in static situation. Where $E \in \Omega^1(U)$, $p \in \Omega^0(U)$, $\ast$ is hodge star operator, $U= \mathbb{R}^3$ ...
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Jackson Electrodynamics: spherical coordinates and azimuth symmetry - potential due to a charge

In Jackson Electrodynamics, chapter 3. We saw that for an azimuth symmetry, we have, $$ \Phi(r, \theta) = \sum_{l=0}^{+\infty} \left(A_l r^l + B_l r^{-(l+1)} \right) P_l \cos(\theta) $$ Then in the ...
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1answer
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Can an electric current be created within a closed loop of wire using an electric field?

I would like to know if a small electric current can be created in a closed loop of wire by using a strong electric field to move the free electrons within the closed loop of wire. To create this ...
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Defining $H$ *magnetic field* in Magnetostatics

This question is related to this other one in math.SE. I'm having troubles studying the "macroscopic" case for a magnetic potential vector and verifying ...
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Why does force between plate capacitors not change when dielectric is inserted between them?

I was told in my physics class that the force does not change between the two plates but wouldnt the electric field not change between them bc it gets divided by the dielectric constant?Hence the ...

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