Electrostatics is concerned with the field and potential of stationary electrical charges and electric charge distributions. Problems are this type are almost exclusively concerned with mathematics of geometries using the inverse-square law.

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48 views

Finding V in a electric field? [closed]

How will we find $V_{ab}$ when $\vec E = (2i+3j+4k)$ N/C , $\vec R_a = (i-2j+k)$ m and $\vec R_b = (2i+j-2k)$ m ? I know $\vec E= -\frac{d V}{d\vec r}$, but I don't know what should be my initial ...
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32 views

Charge Image Problem: Work done on charges on the plate

Assume there is an infinite grounded conducting plane in the $xy$-plane. Assume also that a point charge is being brought slowly from $z=\infty$ to $z=z_0$, slowly enough that the problem is treated ...
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23 views

Why is the Poisson - Boltzmann equation not suitable for high potential?

The Poisson - Boltzmann equation is to find the potential whose charge density obey the Boltzmann distribution. If the potential is not large compare to $k_BT$, the PBE can lead to the Debye–Hückel ...
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2answers
83 views

Meaning of “Grounded”

In my opinion, "grounded" means having the same potential as the potential at infinity, which is usually set to zero. Now if we consider a conductor inside a uniform electric field, what is the ...
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2answers
117 views

Grounded conductor inside a uniform electric field [duplicate]

I am working on a textbook problem of a grounded conductor inside a uniform electric field. The textbook states that "grounded" means potential = 0. In my opinion, "grounded" should mean "same ...
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0answers
14 views

Questions regarding rubbing catfur on glass

I have certain questions regarding the electrostatic charge developed by this rubbing effects: 1-what is the threshold for electrostatic charges by this process? 2-can we define potential energy ...
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1answer
65 views

Finding out the Potential difference

Find the potential inside and outside a uniformly charged solid sphere whose radius is $R$ and whose total charge is $q$. Use infinity as your reference point. Compute the gradient of $V$ in each ...
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1answer
54 views

How is the charge concentrated at the centre of shell for calculating potential from it? [duplicate]

While calculating electric potential due to a spherical shell at a point outside the shell, why do we say that the entire charge is present at the centre of shell? Is this true even if the charge on ...
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1answer
67 views

Integration over $S^2$ in electrostatics

I'm studying for a test in electrostatics and I'm always failing on putting up the correct integrals. In one problem I have the surface of a sphere with radius $a$ and an opening angle of $2\theta$. ...
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3answers
110 views

Capacitance: How to increase total charge drawn from a battery?

I can't seem to find any information about how parallel capacitors or capacitors in a series affect how much a capacitor can charge, not in my textbook or online. Here is the question I am trying to ...
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0answers
39 views

Electromagnetic energy with P and M

In many books, for a linear dielectric medium in which we have Maxwell's equations and the relationships $${\mathbf D}=\varepsilon({\mathbf x}){\mathbf E}$$ and $${\mathbf B}=\mu({\mathbf ...
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2answers
90 views

Electric field of a dipole

I'm trying to find the electric field due to an electric dipole $\mathbf{d}$. There are plenty of approaches to doing this online, but I want to do it "my way," which doesn't seem to be working (and I ...
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2answers
64 views

What will happen when “earthing” is not an option?

I know that earth has a very high capacitance (of about 711$\mu$F) and it would take a lot of time for this but since we earth almost all our appliances for safety, wouldnt one day come when earth ...
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1answer
33 views

Is there a way to induce a net negative electric charge in an electrically conductive material, and If not why?

From what I've been reading, moving electrons don't compress relative to the protons within the atom, For reasons that I'm having difficulty understanding. Seeing that this is the case I would like to ...
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1answer
50 views

Electric field of half a wire

I am trying to calculate the electric field of a half wire in polar coordinates. At $y=R$ is a wire going from $-\infty$ to $0$ with charge density $\rho$. I want to calculate the electric field at ...
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3answers
80 views

Why the electric field inside a conductor is zero? [duplicate]

In electromagnetism books, such as Griffiths or the like, when they talk about the properties of conductors in case of electrostatics they say that the electric field inside a conductor is zero.
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2answers
147 views

Electric potential of spherical water droplet [closed]

I'm trying to answer the following: 1000 spherical water droplets, each of radius $r$ and each carrying a charge $q$, coalesce to form a single bigger spherical drop. If $v$ is the electric ...
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1answer
107 views

Electric Field at surface/side of cylinder [closed]

I know I can use Gauss's law to find the Electric Field inside and outside the cylinder very easily. We can select Gaussian surfaces for different cases (i.e. $r \lt R$ and $r \gt R$, where $R$ is the ...
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0answers
131 views

Infinite chain of alternating charge

The problem There is an infinite chain (1d) of alternating charges that are in a distance a from each other. That is there is one charge +q and next to it -q and so on. Now calculate how much work it ...
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1answer
93 views

Jackson equation 2.9; How to derive it?

I wanted to understand the derivation of Jackson's equation (2.9) that you can find here on page 31 (50/661) from the potential given earlier. This equation is written as: $$ ...
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1answer
61 views

Gaussian surface and and Gauss law

Can we consider a cube as a Gaussian surface, for a point charge located at its center.since,Gaussian surface is a closed surface which has a constant electric field but in this case the both the ...
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2answers
213 views

Grounded conducting sphere inside uniform electric field

The problem of a grounded conducting sphere inside a uniform $E$ field in the $z$ direction can be solved by imagining the field be produced by a pair of charges $Q$ and $-Q$ put on the $z$ axis, ...
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1answer
119 views

How do I place point charges when using the method of images with a sphere?

We have a point charge $q>0$ in vacuum at a distance $a$ from the center $M$ of an isolated metal sphere that has a total charge $-q$ and radius $R$. ($a>R$) A) Use the method of images ...
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1answer
98 views

The force on an infinite line of charge perpendicular to a on a rod of charge

Essentially the question is to calculate the force exerted by a charged rod perpendicular to an infinite line of charge: $\vec{F}_{\text{rod}\rightarrow \text{line}} =\dots$ My question is it okay to ...
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1answer
121 views

Simulate / plot electrostatic field

I have something like this: For given voltage (9 V red wire, 0 V blue wire) I want to simulate electrostatic field. I already know, for example that in the point (10.5;0) there are 10 V and etc. I ...
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40 views

What are eigenfunctions in a box which includes two kinds of medium?

I have to solve a problem of mathematical physics. There is a simple case which can inspire me to solving a more complex case. Considering a metal box in 2D $0<x<a$ and $0<y<b$. And ...
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1answer
93 views

Find the points where potential is null

Let's say we have two charges called $q_1$ and $q_2$, respectively $20 \, C$ and $-40\,C$, at a distance $d=1\,m$ We want to find all the points where electric potential is null. I solved the ...
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1answer
161 views

Boundary conditions of this problem

We have A point charge, a homogeneously charged insulator with total charge $Q''$ which is a ball with radius $R$, a conducting metal ball with charge $Q'$, radius $R$ and a grounded metal (no ...
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2answers
112 views

A little question about Gauss' Law

So I've just learned Gauss' Law a few days ago. I also worked out some applications of Gauss' Law. But I have a little confusion. In a couple of books that I referred, I found a statement that I don't ...
2
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1answer
104 views

Laplace's Equation - under what circumstances does it hold?

I'm currently taking an EM course whereby we deal with systems that satisfy Laplace's equation $\nabla^2 \phi = 0$. Examples include permeable sphere in a magnetic field and metal sphere in electric ...
2
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1answer
133 views

Boundary conditions in Electrostatics

If I have a grounded conducting material, then I know that $\phi=0$ inside this material, no matter what the electric configuration in the surrounding will be. Now I have a conducting material that ...
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2answers
43 views

Coulomb & Electric Fields (Highschool Physics)

If an electric field is said to have a strength of $10^{-15} N/C$, what does this mean? N is Newtons, C is coulomb - I'm not sure how they link? So then I am asked to calculate the force on the ...
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1answer
60 views

Electric field energy

Is it true that $\int_V \rho \phi $ is the equation for the energy of a charge distribution in an external potential and $\frac{1}{2} \int_V \rho \phi$ is the equation for the energy of a charge ...
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2answers
141 views

What is the first non-vanishing multipole moment of this configuration?

Imagine that you have a triangle where each side has the length $a$ and a charge $q$ sitting at every vertex. Additionally, we have a charge $-3q$ sitting in the center of the triangle. What is the ...
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3answers
190 views

Charge On parallel plate capacitor?

Suppose if we supply two plates of parallel plate capacitor with charges $Q_1$ and $Q_2$.What would be the charge of the capacitor? As the field inside plate should be zero and hence using gauss law I ...
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4answers
593 views

Electric Field due to a disk of charge. (Problem in derivation)

This might be a really silly question, but I don't understand it. In finding the electric field due to a thin disk of charge, we use the known result of the field due to a ring of charge and then ...
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2answers
361 views

Gauss’s Law inside the hollow of charged spherical shell

Use Gauss’s Law to prove that the electric field anywhere inside the hollow of a charged spherical shell must be zero. My attempt: $$\int \mathbf{E}\cdot \mathbf{dA} = \frac{q_{net}}{e}$$ $$\int E ...
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1answer
149 views

Neutral shell(with a charge inside) in an electric field

A positive point charge $Q$ is kept eccentrically inside a neutral conducting shell. An external uniform field E is applied. Then: a) Force on Q due to E is zero b) Net force on Q is zero ...
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1answer
60 views

Earnshaw Theorem for ionic solids

Is a single molecule of sodium chloride (say) or a cluster of molecules of NaCl unstable, although macroscopically NaCl is in fact, stable? How can I reason this based on Earnshaw's theorem?
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1answer
52 views

Earnshaw's theorem for extended conducting bodies

I read on Wiki that Earnshaw's theorem has been proven for extended conducting bodies. If we consider the case of a positive charge at the centre of a symmetric metal cavity- the positive charge and ...
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2answers
40 views

Charging a spherical capacitance

How could one charge a spherical capacitor with a battery or any other emf source?
6
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1answer
105 views

Green function two solutions questions

I am having some trouble with Green functions in electrostatics What is the meaning of this trick: Given $$\vec{\nabla}^2 V(\vec{r}) = \frac{-1}{\varepsilon_0}\rho(\vec{r}) = ...
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1answer
165 views

How to find the electric field due to a point charge in 3 dimensions?

A point charge with charge $+q$ is situated at $(x,y,z)$. How do I find the electric field at $(p,q,r)$? $E=k\frac{q}{r^2}$, right? So why isn't the electric field, ...
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2answers
28 views

Stopping an isolated metal ion

If we obtain something like a single isolated hydrogen atom I.e. $H^+$ is it possible by keeping it in a system of charged rings to contain and stop it at the centre of the system? Any positively ...
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0answers
45 views

Electric field due to charge in one direction

I am supposed to calculate the electric field due to the charge density $\rho(x) = Ax e^{-\lambda |x|},$ where the density is supposed to be homogenous in $y,z$ direction. The problem is, that the ...
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1answer
40 views

electrostatics numerical [closed]

Two insulated copper spheres have their centers separated by a distance of 50cm. If charge on each sphere is 6.5×10⁷C, what is the mutual force of repulsion when the spheres are placed in water? The ...
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1answer
40 views

electrostatics particle charging

When ash particles are charged negatively ( corona charging, ionization, tribo electric ) and then collected on to the fabric; particles arrange themselves in porous dendritic structure whereas ...
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1answer
81 views

Charge Distribution On Hollow Sphere

Say we have a hollow conducting sphere (with some finite thickness). If this object has an excess charge amounting to +Q coulomb, and there is no extra electric field in the surroundings (due to ...
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0answers
50 views

Electric Potential Change

Imagine we have a conductor in the shape of a sphere with charge $Q$ on it. The conductor is not grounded. There is an associated potential $V=\frac{Q}{4\pi\epsilon_0 R}$ at and in the sphere, where ...
3
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2answers
135 views

When to use which representation for an electric field

In class we covered three types of possibilities to evaluate the electric field for static problems. Unfortunately, most physics textbooks cover these ways without addressing the question of ...