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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Charge accumulated on a hemispherical bulge on a conducting sphere
Consider a conducting sphere of radius $R$ which has a small hemispherical bulge on the surface of radius $r$. The sphere is given a charge $Q$.
The expression for the charge accumulated on the ...
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Pathways of Dielectric breakdown
I wanted to know if Dielectric breakdown can choose pathways different from its immediate electric field direction for example in the picture
If Pathway 1 is of higher Dielectric Breakdown strength ...
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Estimating dielectric polarization based on supply voltage frequency [closed]
I am currently dealing with a problem which has a series of conductors (assume them to be copper) embedded in a film made of a polyimide material and the film is exposed to air. The conductors are ...
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Charge on a conducting sphere inside uniform electric field after it is ungrounded [closed]
A grounded conducting sphere of radius R is immersed in a uniform vertical electric field E on the z axis. The electric field induces a distribution of charges on the sphere. What is the net charge Q ...
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Why can we just plus two charge directly if they don't connect each other by a wire?
Two concentric infinitely thin conducting spherical shells of radii a and b,where a<b,are charged to potentials $V_a$ and $V_b$ respectively.The inner shell has a charge and the outer shell has a ...
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Electrostatic potential of finite charged wire
So I was trying to find the electric potential at any point $\boldsymbol{x}$ of a charged wire of length $L$ at the $z$ axis, from $-L/2$ to $L/2$, and I had to write it down in terms of elliptic ...
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If two equal and opposite charges are not taken apart why they are considered as neutral? and what is neutral? [closed]
If two equal and opposite charges are not taken apart why they are considered as neutral and what is neutral, charge or field
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The problem of the density of the induced charge on a dielectric cylinder. Why is my solution wrong? [closed]
Why is my solution wrong?
Task:
The dielectric cylinder is in an external uniform electric field E, which is parallel to the axis of the cylinder. Find the surface density of the charges induced on ...
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Solution to Laplace Equation [closed]
Consider two dimensional Laplace equation in cylindrical coordinates
$$\frac{\partial^2 \phi}{\partial^2 r} + \frac{1}{r}\frac{\partial \phi}{\partial r} + \frac{1}{r^2}\frac{\partial^2 \phi}{\partial^...
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Variation of Resistivity After The DIELECTRIC BREAKDOWN VOLTAGE Is Applied
I want to know how a material's resistivity changes after the dielectric breakdown voltage is applied and crossed. Let's say for a circuit after air becomes a conductor for E=30kv/mm what would be the ...
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Measuring electric potential with a flame probe
I'm reading up on an experiment to measure the electric potential at some point in space. There's a charged metal sphere that sets up an electric field in space. We want to measure the voltage at some ...
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General solution to the Laplace equation in spherical coordinates
I'm currently going through Jackson chapters 3 and 4 and don't understand what exactly "$l$" or its physical meaning is when looking at the general solution to the Laplace equation in ...
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In what ways are the charges and surface charge densities distributed when two charged conducting spheres are connected?
When two charged conducting solid spheres(having charges Q1 & Q2) are connected,the charges get distributed in the ratio of their capacitance(C).C∝radius in case of spheres and hence charge ...
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Electrons distribution when a conductor is placed in an electric field
(This is releated to the question of how electric field inside a conductor is zero, but Im trying to focus on a specific part of that expalnation in this question, I hope you understand).
Im ...
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How does 0 electric potential but non-zero electric field work mathematically
I've been trying to figure this out on my own for days and finally decided to start googling. For reference I'm self studying Griffith's E&M textbook. I'm at the part where he derives the equation ...
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Charge distribution on a discharged conductor
Question
I am trying to prove that given a conductor with zero net charge on it then the charges necessarily distributes on its surface so that the density is zero at every point.
We can assume the ...
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Is charge accumulated when two conductors of different resistivity placed in series in an electric circuit?
Let's say two long cylindrical conductors of resistivity ρ1 and ρ2 are joined together and a current I is flowing uniformly through the cross section
So if we consider this scenario two different ...
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If I had an infinite plate would the voltage increase as I get away from it?
Because the equation for electric potential is V=-Es, if I were to have an infinite plane of charge emitting uniform electric field would this mean that as I get farther away from it my potential will ...
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Potential outside two infinite sheets with hole [closed]
Suppose I have two infinite sheets, one having $+\sigma$ while other having $-\sigma$ charge density separated by a distance l. Now, the question made a hole of radius R in each sheet opposite to each ...
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What is the difference between $V=Es$ and $V=-Es$? [closed]
I have been using the equation $V=Es$ for all my calculations and have gotten it right. However, everything now has a negative sign including the equations from online as well as textbooks. When do I ...
user361546
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Do we integrate electric potential when solving for it?
Below I have attached the equation of integrated electric potential. I am confused because through previous practice problems I did, I did not integrate for electric potential or used the dot product. ...
user361546
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Electric Potential Energy of a system of charges: Does it not change at different points?
I understand that potential is for a point/space and potential energy is dependent on field which applies only when we have more than 1 charge.
But please consider this system of charges. Three point ...
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How can a surface charge create field on itself? [closed]
How is the surface charge creating a field on itself ?Grifith has put me in confusion.The example 4.8 of electrodynamics by Grifith shows that the bound surface charge is partly due to the field of a ...
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What is the correct way to visualize potentials when the test charge is negative?
I use this picture to visualize a dipole system. The +ve charge is at a higher potential and -ve charge is at a lower potential. It is easy to explain to someone how a '+ve test charge' kept at ...
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Exchange interaction and nuclear fusion
Most texts about nuclear fusion say that the reason it is so hard to get protons to fuse is the strong Coulombic repulsion between them. However, it seems to me that at close distances, protons should ...
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Electric potential inside insulating shells [closed]
I came across this problem and was very confused by the solution's approach:
A thin spherical shell with radius $R_1 = 4\,\text{cm}$ is concentric with a larger thin spherical shell with radius $R_2 ...
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How to find a No Flow Boundary intuitively or exhaustively for an electric field simulation?
Apologies as this is my first time posting here.
I am trying to simulate Electric Fields and lines of force using pygame to find no flow boundaries. I wrote some crude code and was able to come up ...
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Electric Field Strength due to a hemisphere (Uniformly charged) [closed]
I have a uniformly charged hemisphere. I need to find Electric field due to this at the center of it.
I tried by taking semicircular rings at angle angle $\theta$ and proceeding like this:
Let ...
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Can we compute potential at a point near a uniformly charged rod using these two different routes in calculus?
Consider a uniformly charged rod of length $L$ and a point $P$ on the horizontal line of symmetry, depicted below
The ultimate goal in the calculations that follow is to find the potential at $P$.
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Derivative of the Dirac delta function [migrated]
So, I was reading about the Dirac delta function and how it's differentiation works. So, pretty much all texts and online sources I saw, define it using the integral:
$$ \int_{-\infty}^{+\infty}x\...
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Can we distinguish between gravity and electrostatic forces interacting on celestial bodies?
The orbit of one celestial body around another is thought to be caused by gravity alone. However, could part of the force determining the orbit (at least in theory) be caused by a difference in the ...
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Where do I fail, trying to adapt Gauss law in 2D? [duplicate]
So I went through the Khan Academy tutorial on divergence and flux calculations for an area C encircled by a parametric function $s(t)$.
Here $C$ will be a circle with a radius $r$, centered by a ...
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Energy due image charges
Consider a point charge located above an infinite, grounded, conducting plane. The potential everywhere above the plane is the same as that of the image charge (located below it). Why is it wrong to ...
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What do electric field lines tell us?
Does it indicate the direction of motion of the photons in electrostatic fields (I mean is the direction of the electric line of force the same as the direction of motion of the photons at that point) ...
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Understanding intricacies of a simple example involving electric potential and potential energy of a system of two charged particles
I've been studying the concept of electric potential and though I thought I had understood it, I just found myself in a tangle.
Consider a positive charge $q_s$ located at the origin of our coordinate ...
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Electric field inside a continuous charge distribution
Suppose that I have a continuous charge distribution that occupies some volume $V$, and my goal is to find the electric field inside of it, One way to approach this is by pretending that $V$ is made ...
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Multipole expansion along a ring [closed]
I'm supposed to calculate the behavior of the electrostatic potential $V$ at large distances $|r| \gg a$ for the following linear charge density along a ring of radius $a$:
$$\rho(r,\psi, z) = \frac{q}...
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Static fields with the finite-difference time-domain (FDTD) method: Is it possible?
Can the FDTD method be used to solve electrostatic fields? If yes, how can an "electrostatic field source" be imposed?
Details:
The finite-difference time-domain (FDTD) method solves the ...
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Multipole expansion - different derivation leads to the dipole decreasing in $r^{-2}$ and $r^{-3}$
To prepare myself for the electrodynamics course i used Griffith, in which his derivation gives
$$V(r)=\frac{1}{4\pi \epsilon_0}(\frac{1}{r}\int \rho(r')d \tau ' + \frac{1}{r^2}\int r'cos\alpha \rho(r'...
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Is the Electric Potential infinite above a surface with a charge density $\cos(x+y)^2$ everywhere on the $x$-$y$ plane? [closed]
Suppose we have a charge density $\sigma (x,y) = \cos(x+y)^2$ everywhere on the x-y plane. The distribution of charges should look like constant stripes running along the $\vec{x}-\vec{y}$ direction, ...
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How to view electric charges creating electric fields
What is the best way mentally think of how a particle with electric charge creates an electric field? Is it to think that field lines propagate, extend, radiate (whatever verb you want to use) etc., ...
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Charges outside a sphere - existence of a stable equilibrium?
I was just thinking if we have a sphere that contains some charges inside and now we have a point charge outside the sphere, would there be any configuration that would allow for a stable equilibrium ...
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Trick question: why do dielectrics and isolated conductors affect capacitance differently?
This question confused me a bit, but I figured out the answer. I just want to share this trick question here.
Trick question: Dielectric material produces net surface charge when placed in electric ...
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Materials of continuous charged distributions
I have seen some related questions about this, but none of them actually answered mine. In electrostatics, one usually wants to consider the electric field of a continuous charged distribution, such ...
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Electric field on a small sphere too large
I used the Fermi energy for a given material to find the number of free electrons found on it's surface:
Where the Fermi energy E_f was given from another calculation using band theory. The solution ...
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Why is $dq=\rho_s a d\theta 2 \pi a \sin\theta $ in the semi-sphere?and $E_z=\int^{\frac{\pi}{2}}_0dE_z$ not $\int^{\frac{\pi}{2}}_0$? [closed]
There is a semi-spherical equation $x^2+y^2+z^2=a^2,$ and $z>0$, and the surface charge density is $\rho_s$. Please calculate the size and direction of the electric field generated by the charge ...
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Electric flux, is q/absolute permitivity, but is also cross product of electric field and area vector, then why doesnt it increase with radius? [closed]
A charge q is enclosed by a gaussian spherical surface of radius R if the radius is doubled the outward flux will remain the same. How is that possible if flux is also defined as the cross product of ...
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About kinematics of electrons in a circuit
We know that electrons flow in a circuit due to the electric field, so shouldn't the electrons be accelerating, but we also know that
$i=neAv$ so from here we can conclude $v=i/neA$ which is a ...
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How is voltage generated and maintained in a circuit?
I recently discovered this answer which explains how batteries maintain a constant potential difference. So what I understood was that batteries spew out electrons on the cathode, and by doing this ...
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Infinite boundary in uniqueness of poisson's equation in electrostatics?
When using the method of image charge, It seems to me that we are using the following "version" of the uniqueness theorem:
Let $D \subset \mathbb{R}^3$ be a region. Suppose we have two ...
