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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Work of discharge capasitor [closed]

when a capacitor discharge means that potential difference is equal to 0; The Work is equal to -dU? where dU is dynamic energy
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What is the work of a capasitor? [closed]

on a capacitor with a given surface charge density the work equals the relation 1, on a capacitor with constant potential difference the work formula is relation 2. Can you explain the difference ...
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Change electric potential along uniform electric field

I have a doubt. I do know that the potential at a point decreases as we move in the direction of electric field because $$V=\frac{KQ}{r}.$$ This was taught to me with a point change as an example. I ...
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Potential of a capacitor

I'm learning about capacitors, and i cannot visualise what potential difference of the capacitor is. I do know that potential of a charge is work per unit charge which is (kq)/r , where q is the ...
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Can we say that there exists an upper bound to which heat dissipation can be minimized in pulling the plates apart of an ideal capacitor reversibly? [closed]

So I thought like this, As we know, $$dw = du + dq.$$ Now, internal energy is change in microscopic potential energy and kinetic energy Assuming, all change in internal energy to be change in electric ...
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Closest distance of approach [closed]

Suppose a charged body $q_0$ is at rest. Another charged body $q_1$ at infinite distance starts moving towards $q_0$ with velocity $v_1$. Gradually the velocity of $q_1$ will decrease and that of $q_0$...
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Charge accumulation on surface of solid sphere due to placement of dipole inside cavity

This is the case when a plus q charge is inside cavity (with same centre) of a spherical solid conductor. Everything is uniform. But what will it be like in second diagram I think the external ...
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Clearly expression in electric field strength

For a uniformly charged disk the field strength in z axis(z axis passes through the center of disk) is equal to $ε(z)=(\frac{2KQ}{a^2}) (1-\frac{z}{\sqrt{a^2+z^2}})$ In case $z\gg a$, $ε(z)= \frac{2KQ}...
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Disagreements in derivations of electrostatics

In the derivation of the potential energy of electrostatic systems we get (I am working in cgs) $$W=\frac12\int\phi\,dq=\frac12\iiint\phi\rho\,d V \tag{1}$$ But $$\vec\nabla\cdot\vec E=4\pi\rho$$ Thus ...
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How is the work done by a battery (when connected to a capacitor) independent of time?

We know that W bybattery = V(It) = VQ, which is time-dependent. But when the battery is connected to a capacitor then W bybattery = 1/2 (CV^2), where C and V both are time-independent, hence W ...
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Classic Image problem

The classic image problem: Here, to calculate the potential above an infinite grounded conducting plate and a point charge q held at distance d above the plate, the image method is used. Here, I want ...
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Does a perfect conductor has unlimited supply of charges?

In Griffiths, it has been written that A perfect conductor would be a material containing an unlimited supply of completely free charges. My question is, how is the unlimited supply of charges ...
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Gyromagnetic precession of electron inside a homogeneous electrostatic field?

Would an electron placed inside a homogeneous electrostatic field (i.e. the static field between the parallel plates of a fully charged capacitor) in addition to being accelerated towards the ...
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Different answers for self-energy?

If we calculate the self-energy using the energy density integral then we get $$U=\int^\infty_0\frac{q^2}{8\pi\epsilon_0 r^2}dr=-\frac{q^2}{8\pi\epsilon_0 r}$$ However, since the potential of a point ...
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Consistency of existence of point charges and energy in fields

In Feynman lectures, Volume 2 chapter 8 (https://www.feynmanlectures.caltech.edu/II_08.html#Ch1-audio) at the very end Feynman remarks We must conclude that the idea of locating the energy in the ...
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How do we know that the electric field exists when there is no other charge nearby?

We have defined the electric field to easily calculate the force exerted by a system of charges on another charge. What happens to the Electic field if the test charge is removed? Does it still exist ...
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Why is the total electrostatic energy bigger than the sum of separate energies?

I don't understand why, if we add the two energies $\,\boxed{1}\,$ and $\,\boxed{2}\,$ from two electric fields, the component $\,\boxed{3}\,$ is added and so it's different from their sum \begin{...
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Finding the interaction energy of two spherical charge distributions [closed]

A question asks for the total electrostatic energy of a system of two uniformly charged hollow insulating balls of different radii (say $R_1$ and $R_2$) and charges (say $Q_1$ and $Q_2$), placed at ...
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Why is method of image charges not working?

suppose a situation with two infinite thin conducting planes in front of each other with one of them having a charge density σ it can be clearly predicted that the induced charge density on neutral ...
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How to intuitively interpret the dependence of temperature and density on Debye Length?

I am learning plasma physics through Chen and in the first section it discusses Debye shielding. Essentially, if you place a test charge in a plasma such that it generates a positive potential $\phi_0$...
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What will happen if one electronic charge is given to a conductor?

I was taught in my physics class that if some charge is given to a conductor then the charge gets distributed over its entire surface. But what will happen if just an electron ( a point charge) was ...
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Complex permittivity and density flux time response expansion

I've been studying complex permittivity and come across to expansion 3.4.2 on website https://phys.libretexts.org/Bookshelves/Electricity_and_Magnetism/Book%3A_Electromagnetics_II_(Ellingson)/03%...
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Why does changing the permittivity of the dielectric within a capacitor not have any effect on the electric field opposite the plate?

Utilizing FEMM 4.2, I built a pair of simple parallel plate capacitors, however I oriented them so that the anodes of these capacitors faced each other. As expected, the electric fields of the two ...
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Discharging capacitor: Series vs Parallel

Pretty basic stuff, but to be honest I haven't found a circuit diagram showing a capacitor discharging in parallel. The only scheme I can come up with is shown here: $\color{gray}{\textbf{[ Edited ]}}$...
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Electrostatic energy of capacitors and point charges

A number of questions have previously been asked about electrostatic energy for a system of conductors. But I am still confused about this topic. Suppose we have an ideal capacitor consisting of two ...
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Anti-gravity effect from charged capacitor? (correction)

A Reddit user called GratefulForGodGift has hypothesized that an electric field could warp spacetime. Consider the electrostatic field energy $\epsilon$ stored in a parallel plate capacitor given by: $...
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Arbitrary Constant in Electric Potential

Consider an electric potential that is the result of a superposition of two electric potentials: $$\Phi = -\frac{1}{4\pi \epsilon_0}\left[\int_{O}^bE_1 \cdot dr+\int_O^bE_2 \cdot dr\right].$$ If we ...
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Follow up question to "Why is the Earth's potential taken to be zero?"

I am questioning the validity of the problem posed in Why is Earth's potential taken to be zero?. The problem is stated as: "There are two thin concentric conducting shells of radius 𝑎 and �...
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Why can we add the two terms in the Lorentz force?

The term "Lorentz force" in the title refers to (1). my textbook states: The Coulomb force is mediated by the electric field and acts on the charge $q$, that is, $\mathbf{F}_e = q\mathbf{E}$...
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Microscopic explanation for the linear relationship between the Coulomb potential and the effective Coulomb potential

The Coulomb potential a distance $r$ from a point charge $q$ is $$ \phi = \frac{1}{4\pi\varepsilon_0}\frac{q}{r}\,. $$ Here $\varepsilon_0$ is the permittivity of vacuum. Now assume that there are ...
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Why is Earth's potential taken to be zero?

This is not a duplicate question for many similar questions, I have tried finding an answer to this everywhere but to no avail. So here is my problem: Why is Earth's potential taken to be zero? Now I ...
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Questions about Maxwell capacitance matrix and reference point selection

Let's consider a system of n conductors. If I'm not mistaken, the Maxwell capacitance matrix tells us that the following system of equations applies: \begin{align} Q_1 &= C_{11}V_1 + C_{12}V_{12}...
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Where magnetism arises from?

Imagine we have a test charge and we push it, reaching a constant velocity of $u$. Now the electrons inside of the cables reach a velocity of $v$. Our goal is to measure the electric field that the ...
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Electric Current Misunderstanding

There are examples that describe electrical potential as two oppositely charged plates facing each other to make an electric field. They place a positive test charge close the positive charged plate ...
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Gauss Law for finite linear conductor

Why can't Gauss Law be applied to a finite linear Conductor, while as the same can be applied to an infinite Conductor.
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Most Stable Orientation of Ellipsoidal Conductor in Electric Field

As described in the question title, say we have an ellipsoidal conductor where all three axes are of different length, and we place it in a uniform field. What is the orientation of the ellipsoid ...
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Electrostatic self-interaction of two multivariate Gaussian charge densities

I'm trying to figure out the following question: If $\mathcal{N_1}(\vec x|\vec \mu_1, \Sigma_1)$ and $\mathcal{N_2}(\vec x|\vec \mu_2, \Sigma_2)$ are two arbitrary multivariate Gaussian charge ...
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Are other terms in multipole expansion other than the monopole term always there?

My question is whether the remaining terms other than the monopole actually always there and we consider only the monopole for convenience purposes (because it is the most dominant term) or they ...
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Why is there no physical interpretation to non-real potentials in classical electromagnetism?

In Griffiths 4ed, he solves Laplace's equation and omits one of the solutions because it is imaginary. What are the grounds on which imaginary solutions or values can be marked as "non-physical&...
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Orthogonality condition for spherical harmonics

The 3ed of Jackson E&M states the following as the orthogonality relationship for the spherical harmonics: $$\int_{0}^{2\pi}d\phi\int_0^{\pi}\text{sin}\theta d\theta \space Y^*_{l'm'}Y_{lm}=\...
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Potential Distribution in Container with 2 Electrodes?

Suppose I have two electrodes (modelled as point electrodes) inside a finite rectangular prism container, and I connect the electrodes to a DC power supply, such that one of the electrodes can be ...
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2 answers
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Multipole moments of line charge

I am supposed to calculate the multipole moments of a line charge with total charge Q spread from $z=-a$ to $z=a$ on the z-axis. I know that each multipole moment is given by: $$ q_{l,m}=\int_{\mathbb{...
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Dependency on capacitance [closed]

We know that when capacitance of a capacitor changes,it means the distance between the plates changes and as potential difference of the capacitor is dependent on the capacitor, i.e ($V=Ed$), the ...
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How the Product of Electric and Magnetic field equals Tangential component of Electric field

Considering the Equations, where E_theta & E_r represents the tangential and radial components of Electric field. Now by taking the ratio we get the following equation . Now using Poynting Vector,...
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Electric Field of a uniformly charged sphere

I'm calculating the eletric field of a uniformly charged sphere so that I can compare it with the potential of a uniformly polarized sphere. So I calculated using the eletric displacement, $\...
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Is Laplace's equation valid in presence of point dipole?

In the presence of point dipoles in a region of interest, can I say that the charge density at the dipoles' positions is zero and hence Laplace's equation is valid and can be solved with separation of ...
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What is the pressure apllied to liquid in sealed tank?

I have a sealed tank positioned on a high surface filled with water and nitrogen gas above. Tank manometre shows pressure of 0.5 bar. What is the pressure applied to the water in tank? Is it 0.5 or 1....
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Helmholtz’s theorem and electrostatic charge density

According to Helmholtz’s theorem, the electric charge density has to go to to zero as r goes to infinity faster than 1/r^2 to be able to construct an electrostatic potential function, yet I don't ...
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2 answers
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Why is the Curl of a non-uniform electric field still 0?

So I intuitively think about taking the curl as, taking a step perpendicular to the direction the vector (describing a field at a point in space) is pointing in and seeing how the field changes. If ...
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Is there another way to prove that the electric field inside of a conductor is 0 without using Gauss' law?

Suppose there is a spherical shell conductor with a stationary negative charge placed inside. The shell has finite thickness so in order to make the field inside of the conductor 0, positive charge ...
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