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 [tag:electromagnetism] and/or ...

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Where is the flaw in deriving Gauss's law in its differential form?

From the divergence theorem for any vector field E, $\displaystyle\oint E\cdot da=\int (\nabla\cdot E) ~d\tau$ and from Gauss's law $\displaystyle\oint E\cdot ...
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2answers
514 views

Gauss' law giving zero field where field is not zero?

Two plastic sheets with charged densities as shown: I'm trying to find the field at $B$. I obtained the correct answer by adding up the fields created by each charge density. But I realized that ...
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1answer
84 views

Coulomb's law with an $r^3$, not $r^2$, in the denominator [duplicate]

I am reading an older physics book that my professor gave me. It is going over Coulomb's law and Gauss' theorem. However, the book gives both equations with an $r^3$, not $r^2$, in the denominator. ...
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3answers
221 views

Electric field or static electric field around a plugged-in lamp cord (when lamp is not turned on)?

When an electrical cord from, say, a lamp, is plugged into an AC wall socket, I'm aware that an electric field forms around the entire length of the cord and even before the lamp switch is flipped on. ...
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1answer
47 views

Physical meaning of the separation constants in Laplace's Equation for Electrostatics

In Electrostatics, if we consider a region without charges the electrostatic potential $V$ obeys Laplace's Equation $\nabla^2 V = 0$. We can tackle this with separation of variables. In cartesian ...
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431 views

Calculate the flux of a point charge with Gauss's law

I know from my class that to calculate the flux of a point charge with Gauss's law, I have to make a surface that intersects with all of the flux lines resulting from the charge, and then make this ...
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2answers
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Relationship between surface density and volume density

Often in an E&M problem, I'm having to "chop" an extended object into an infinite sum of smaller extended objects which I know more about to find a potential or electric field or whatever. The ...
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2answers
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Potential energy of a dipole in a uniform electric field convention?

When finding the potential energy of a dipole in a uniform electric field, I was told by my lecturer that the convention is that the potential energy is 0 when the dipole moment and electric field ...
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1answer
124 views

Why do we consider the electric field of an infinite plane? [closed]

I never understood why one would calculate the electric field surrounding an infinite plane, if such thing does not exist. Is there physical motivation for using this model? Are the results applicable ...
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2answers
134 views

Absolute value in the argument of a logarithm

I am wondering how the author rationalizes the removal of absolute value bars around the quotient argument of a natural logarithm. My take on this is that the potential at point $b$ MUST be greater ...
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4answers
352 views

Why does $E=\nabla\phi$ follow from $\nabla\times E=0$?

I understand that using one of Maxwell's equations, $$\vec{\nabla} \times \vec{E}(\vec{x})=0,$$ it can be said that $$\vec{E}(\vec{x})=-\vec \nabla \phi(\vec{x}).$$ However, I can't find or ...
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2answers
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Do black holes have charges?

Do black holes have charges? If so, how would they be measured? Also, does electricity behave the same way? Black holes affect photons, which are carriers of EM radiation, so do black holes have any ...
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7answers
879 views

Why do two ends of a long conducting wire have the same electric potential?

I am not seeing the "big picture" here. If I have two conducting spheres separated by a long conducting wire, why would the spheres share the same electric potential? I think of the spheres as point ...
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1answer
137 views

Why is the force on the charge at the tip of a cone infinite?

Imagine a charge $q$ that is located at the top of a hollow cone with a surface charge density $\sigma.$ The slant height is $L$ and the charge $q$ sits at the vertex of angle $2\theta$. We are ...
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2answers
94 views

Calculating effective capacitance of a circuit [duplicate]

Please refer to the image below. The question asks: 'The effective capacitance between terminals A and B in the network shown in the adjoining figure is?' Here is my working: (C5 and C6 connected ...
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1answer
65 views

Is the sea of electrons in a metal at rest when the metal is in electrostatic equilibrium?

It is said that charges inside a metal in electrostatic equilibrium are at rest, and are stationary. However, don’t the electrons have their own thermal vibrations and whatnot? Aren’t they always ...
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2answers
246 views

What is meant by “unique direction” in most of the arguments in application of Gauss' Law?

This term is really bothering me a lot. While explaining the radial direction of electric field of a uniformly charged sphere, my book writes: Notice the use of argument of symmetry. There is no ...
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1answer
197 views

How did Feynman prove that energy cannot be extracted from electric field?

In the Feynman Lectures, vol. II, chapter 4, Feynman discusses electric potential and says: If we carry a charge from point $a \to b$, $$W = -\int_{a}^{b} \mathbf{F} \cdot ds.$$ Now, in general, ...
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1answer
207 views

Can an electric field align water molecules?

Water is a polar molecule, which means it has an uneven charge distribution. How much of an electric field strength would it take to align all, or most, of the molecules at room temperature?
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1answer
113 views

Usage of Poisson's equation?

I revisited electrostatics and I am now wondering what the big fuzz about Poisson's equation $$\nabla^2 \phi = -\frac{\rho}{\varepsilon_0}$$ is. Wiki says One of the cornerstones of electrostatics ...
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2answers
244 views

What is the minimum distance between two opposite point charges

In an overly simplistic model if I have a single negative charge, and a single positive charge they will be attracted. I expect they will fly together. Click. Good luck getting them apart. The ...
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3answers
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Why isn't the electrical field between two parallel conducting plates quadrupled?

For the sake of clarity and brevity, here is the description from my textbook (Halliday & Resnick 9th): This description states that the electric field is doubled. I am seriously confused. When ...
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4answers
190 views

Why change in Capacitance?

I do know it that the overall capacitance decreases if two or more capacitors are connected in series,but do not understand why? I do understand it mathematically but don't get the physics behind it.
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1answer
456 views

Spherical harmonics

Given the following potential: $$V(\theta,\phi)=\frac{Q}{a}\left(\sin\theta \cos\phi+\frac{1}{2}\cos^2\theta\right)$$ on the surface of a sphere of radius $a$ I am trying to solve Laplace's Equation ...
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5answers
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2 dimensional Coulomb's law equation

We can notice that in the Coulomb's law equation, $$\begin{equation}\tag{1}F=\frac{1}{4\pi\epsilon}\cdot\frac{q_1q_2}{r^2}\end{equation} $$ $4\pi r^2$ factor in the denominator expresses directly ...
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1answer
414 views

Coulomb force on the center of a hexagon?

Six point charges $q$ are at the corners of a regular hexagon that has sides of length $a$. What is the force on another charge $Q$ which is located in the center of the hexagon? What is the force on ...
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2answers
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Calculating the field of an infinite flat sheet of charge using the superposition principle

I am trying to calculate the field of an infinite flat sheet of charge (a plain with uniform charge density $\sigma$) using the superposition principle. I know that the field of an infinite line ...
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1answer
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How to find electric scalar potential of infinite wire with Poisson/Laplace equation?

I though it will be easier then calculating the electric field and then integrating, but I am stuck. lets say we have an infinite wire, charged $\lambda$ per unit of length and its located at the ...
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3answers
937 views

continuity of the electric potential due to a surface charge

The Electric potential due to a charge distribution on a surface is : $\Phi \left ( x \right )=\int \frac{\sigma \left ( {x^{}}' \right )dx{}'}{\left \| x-x{}' \right \|}da$ I want to show that it's ...
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1answer
91 views

What happens to this energy of the capacitor?

Let's say you have a charged, isolated parallel plate capacitor with a certain voltage. My book says that if you insert a dielectric, the voltage drops. However, that would require the energy between ...
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4answers
360 views

Capacitance of a capacitor

Why does the capacitance of a capacitor increase if the distance between the two plates of a parallel plate capacitor is decreased? I think, with decreasing distance between the two plates, the force ...
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1answer
3k views

Gradient of the electric potential

I was wondering if for a point-like charged object, does the gradient of the electric potential point in the direction of maximum increase or maximum decrease of the function $V$?
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3answers
2k views

Why can we use Gauss' law to compute electric field?

For simplicity I'm considering only the sphere case. In the Gauss' Law formulation we have some field $E$ introduced by charges $Q$ inside some sphere, then we compute flux and integrate, and we get ...
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1answer
307 views

Electric Flux Contradiction

I am currently reading about electric flux; and from this passage I am reading, I am sensing a bit of a contradiction: "If the E-field is not perpendicular to the surface area, then the flux will be ...
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3answers
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What are the applications of Gauss's law in technology? [closed]

Freshmen physics textbooks use Gauss's law plus symmetry to calculate the electric field. I was wondering if this method of finding the electric field using a symmetry is used in real applications in ...
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1answer
1k views

Calculating dust attraction to a charged surface

Even though dust particles are neutral, they tend to be attracted to a charged surface. I am guessing this is due to charge induction. Is there a way I can compute the attraction? how will it vary ...
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2answers
323 views

Scale invariance symmetry as a simple argument in an electrostatics problem

In the comments to this post, it was hinted that proving that the force acting on a charge at a vertical distance from a uniformly charged plane is independent of that distance can be done by ...
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2answers
656 views

In which cases is it better to use Gauss' law?

I could, for example calculate the electric field near a charged rod of infinite length using the classic definition of the electric field, and integrating the: $$ \overrightarrow{dE} = \frac{dq}{4 ...
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3answers
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How can I theoretically describe the potential between two capacitors in series?

Suppose to have two capacitors in series: The voltage in the middle point will be: $$ V_X = V_1 \frac{C_1}{C_1+C_2} $$ How can this be explained? It's been asked in electronics, and explained in ...
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2answers
196 views

Differences In Potential Equations

Could someone please describe the differences between the uses each of these potential equations: Potential due to a point charge: $V = \frac{k \cdot q}{r} - \frac{k \cdot ...
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2answers
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What is the effect of temperature on electrostatic-gravitational balance?

We have two identical massive metal spheres at the same temperature at rest in free space. Both have an identical charge and the Coulomb force [plus the black-body radiation pressure if the ...
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2answers
50 views

How do two metal balls of radius $r$ kept at a large distance form a capacitor? [closed]

So this is something really new to me. I have learnt of plate capacitors, cylindrical capacitors, single spherical capacitors, etc. but that to, of finite distance between them. Also please explain if ...
2
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2answers
53 views

Are charges always uniformly distributed on conductors?

As the title says. For example, if I take a fat metal wire with non-negligible thickness, and then wind it into a spiral, but such that none of the parts touch one another (there are no topological ...
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1answer
71 views

Do Dipole Moments Obey Superposition?

Essentially, I have two surfaces which I know how to find the dipole moments for. I realize that $V_{dip}(r) = \frac{1}{4\pi \epsilon_0 r^2} \mathbf{\hat{r}} \cdot \int \mathbf{r'} ...
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2answers
525 views

What makes Human a Conductor

Conductors, are those which have free electrons... and because of this have same electric potential all over. But considering our body, which has many electrical voltage, current signals passing by in ...
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3answers
176 views

Shielding of electric and gravitational force on particles inside a spherical shell

A cavity inside a conductor is shielded from outside electric influences. But, if you put charges inside the cavity, the exterior of the conductor is not shielded from the fields by the inside ...
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1answer
91 views

Can a static electric field have a vector potential field?

We know very well that static electric fields have scalar potential fields, and magnetic fields can't have scalar fields, as $$\nabla\times \vec{B}=\mu_0\vec J$$ $$\Rightarrow \int\nabla\times ...
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3answers
77 views

Does the equation CV = q break down when V is small or a wire is very long?

I'm trying to understand how the equation $CV=q$ relating the voltage difference and charge stored on a charged capacitor breaks down under extreme circumstances. In most problem statements that I'm ...
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152 views

Potential of an infinitely long cylinder

Suppose I have an infinitely long cylinder with radius $R$, charged with longitudinal density $\lambda$. I want to calculate the potential outside the cylinder. The field induced by the cylinder is ...
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2answers
256 views

Continuity of electric field

I was solving a problem in which i came across a radially symmetric discontinuous electric field, which puzzled me for a moment but then I figured that there must be surface charge density at the ...