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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Addition of forces in dielectric material

In this paper (page 2 of document) it is said that: Because this calculated force was comparable to the gravitational force, they assumed that the same would be true for the forces on a ...
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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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Finding voltage between two points in space

If electric field vector is defines as : $\vec{E} = \frac{V_0x^2}{a^3} \vec{i_x} + \frac{V_0y}{a^2} \vec{i_y} $ where $V_0 $ and $a$ are known constants, $\vec{i_x}$ and $\vec{i_y}$ unit vectors of ...
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Electric Field Resulting from a Conductor

In preparation for an upcoming exam, I've been attempting to visualize the electric field produced by a conductor in a variety of situations. I asked myself the following question and attempted to ...
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1answer
58 views

The “classical radius” of the electron [on hold]

According to one theory, the mass m of the electron arises simply as a consequence of the electrostatic energy of its electric field, through Einstein's famous expression ε=mc^2, where ε is the field ...
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33 views

Net Electric Field of Multiple Charges [on hold]

Question: Four charges, each of magnitude +Q are placed at the corners of a square of side a. Obtain an expression for the electric potential at the centre of the square and at the mid point of one ...
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32 views

Why is voltage multiplied when batteries are connected in series but not in parallel?

As i understand, the different voltage between two object is caused by the total different charged between two object. Thus, the higher extra electron between two opposite charged object, the higher ...
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Electrostatics and Current Electricity [closed]

A ball of mass 9 × 10^-5 kgs carries a charge of 5 micro coulombs. What must be the charge in another ball placed directly 2cm above the given ball such that they are held in equilibrium.
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67 views

How does EM radition depend on the reference frame?

In special relativity, magnetism is electrostatics in a different reference frame. This is how we explain the magnetic field being produced by moving charges (aka currents). Charges that move produce ...
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Show the equivalence of two electrostatic energy

$$U = \frac{1}{2}\iint_{all space}^{ } \frac{\rho(1)\rho(2)}{4\pi\epsilon_{0}r_{12}}dV_{1}dV_{2} $$ and $$U = \frac{\epsilon_{0}}{2}\int_{allspace}^{ } \vec{E} \cdot \vec{E} dV.$$ In the left ...
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51 views

Relationship between polarization density and electric field

Imagine I have an electric field $E$ created due to some free charges. Then I introduce a dielectric material somewhere. What confuses me is the polarization field $P$, which is now proportional to ...
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1answer
44 views

Why does the earth suck both positive and negative charges?

If the earth is a bit negatively charged, it is understood that it can take away the positive charges of a positively charged body when grounded. Why does it take away the extra electrons of a ...
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Electric field of Symmetric Parts [closed]

So I'm preparing for a test and one thing that I haven't seen examples of, but know is possible is using Gauss's Law on objects that have symmetric parts. I made up the following question: Find ...
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3answers
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Deriving relationship between distance and angle for field of a line charge

The relationship $r\,\mathrm{d}\alpha = \mathrm{d}x \cos(\alpha)$ is not obvious to me. In fact, when I look at it, I think it should be $r\,\mathrm{d}\alpha \cos(\alpha) = \mathrm{d}x$. Can someone ...
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Vector of electric field

I have a triangle whose points are in $A(0,0,0)$, $B(a,0,0)$ and $C(0,a,0)$. The edges of this triangle are uniformly charged with value $Q'$ and everything is in vacuum. I need to find the vector of ...
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1answer
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Why in PN junctions the octet rule is dominating electrostatic repulsion?

The depletion region in PN junctions is created by charges from the N part diffusing into the P part, thus completing an octet of covalent bonds in the P part. This shift however leaves positive ions ...
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Capacitance in a parallel plate cap with the real electric field

In many books of general physics, they prove the equations for capacitance of a cap of parallel plates as if the electric field where constant everywhere but what would happen if we take the real ...
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48 views

Finding charge density from from differential form of gauss law

I didnt get why he didvided and multiplied by r^2.This question is from d j griffith .
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Divergence in interaction between induced dipoles

Suppose I have two polarizable point-particles 1 and 2 arranged on the z-axis and separated by $r$. Each particle has a dipole moment $\mathbf{p}_i=\alpha \mathbf{E}_i$. If we apply an external field ...
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Potential due to a continuous charge distribution on ring

Derive the formula for the potential at point $P(0,0,z)$ directly above the center of a ring of charge with radius $R$ and uniform charge density $\lambda$. My attempt: Since $$\lambda= ...
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1answer
44 views

How is it possible for an infinitely large charged plane to cause the same electric field regardless of distance? [duplicate]

Assume there is an infinitely large plane with a charge density $\sigma$. I understand how to derive, using Gauss' Law, that $E = \frac{\sigma}{2\epsilon_0}$ is the electric field at a distance $r$ ...
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2answers
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Confusion with Grounded Conductor: bringing in a point from infinity

Suppose, for sake of argument, we have a spherical grounded conductor at the origin. Additionally, let our reference voltage be at infinity. Now, I view the potential of a point in space as being the ...
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Differential equation of a Green function for a dielectric with a charge [closed]

adding Suppose there are two infinite planes, one in $z=a$ and the other in $z=b$, with $a<b$. Between the planes, there is a dielectric medium with constant $\epsilon_1$. The differential equation ...
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2answers
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Gauss law in integral form

Scanning through the lecture notes of my professor I came across some confusing definition, that he calls "Gauss law in a global form" which has the following representation ...
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1answer
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Zero divergence of Electric field

I'm trying to rigorously derive the integral form of Gauss's law from Coulomb's law and the divergence theorem. Arrive at $$ \oint\limits_{\partial V} E\cdot da = \begin{cases} \frac ...
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Field and Charge densities in two dimensional corners and along edges

In jackson's book, we can derive the equation as following. $\sigma(\rho)=\epsilon_{0}E_{\phi}(\rho, 0)\approx-\frac{\epsilon\pi a_{1}}{\beta}\rho^{(\pi/\beta)-1}---(2.75)$ My question is there are ...
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Help regarding understanding derivation of electrostatic potential in a solution to a problem

I was looking at the solution of finding the energy stored in a charged solid sphere in which the electric field was and then later stated the electrostatic potential is I understand that to ...
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2answers
36 views

Equivalent formulas for electric current density

I am reading an article that states that the "ratio of current to the area for a given surface is known as current density" and is defined as $J = \frac{I}{A}$ where $I$ is the current and $A$ is ...
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1answer
21 views

2 spheres both negative or positive [closed]

Two small charged metal spheres A and B are situated in a vacuum. The distance between the centres of the spheres is 12.0 cm, as shown in Fig. 4.1. The charge on each sphere may be assumed to be a ...
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1answer
32 views

What is the purpose of the metal strip??

Context: Two large, flat metal plates are held parallel to each other and separated by a distance $d$. They are connected together at their edge by a metal strip. A thin plastic sheet ...
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Is there a charge across all space? [duplicate]

We're studying electrostatics in class, and the teacher introduced us to Gauss' Law a few days ago as $$\int \vec{E} \cdot \mathrm{d}\vec{A} = \frac{Q}{\epsilon_0}$$ Now suppose that the entire ...
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Two uniformly charged spheres are superposed with slight displacement. What's the surface density?

*Note: This is from the Second Volume of Feynman's Lectures on Physics : Mainly Electromagnetism and Matter And this is the excerpt from the book: If the relative displacement of the two spheres ...
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What is the electric field near an infinite sheet with a point charge near by? [closed]

The electric field near a negatively charged conducting infinite sheet is $\frac{-\sigma}{2\epsilon}$. If we add an equally charged positive particle some distance $r$ away from the sheet, the field ...
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1answer
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Can a human be killed by electro-static discharge while performing daily chores? [closed]

During freezing-winter seasons, as soon as I reach my office and get off the warm-clothing; I get an electrostatic discharge whenever I touch a metallic water-fountain in my lab. The shock I get is ...
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Parallel plate capacitor

How does a parallel plate capacitor emit a constant electric field between its plates? Isn't the electric field governed by an inverse square law? Then what would happen if I put a charged particle ...
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In low voltage (3-12V) DC applications, which is safer to be exposed or touchable + or - terminal?

The - side has a surplus of $e^{-}$s and the opposite is true for the + side of the power supply. Does it not matter, or depends on your configuration / contact with Earth? Please explain!
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How does an electron undergoing uniform circular motion exactly lose energy?

One of the main reasons for the failure of the Rutherford model of atomic structure, it is famously stated, is that the electron undergoing circular orbit loses energy since due to its centripetal ...
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Does Gauss' Law apply to real physical solid conductors?

In a conductor there is no electric field because there is no charge. There is no charge inside because any charges present inside would repel each other and be driven to the surface of the conductor. ...
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1answer
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Binding Energy of an Electric Dipole

My question is structured in two parts: Is there any way to isolate the charges of an electric dipole? What is the binding energy of an electric dipole? To put it in another way, is there ...
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How come we talk about gravitational potential energy and not gravitational potential?

With regards to gravity the equation learned is $$U=-\frac{GMm}{r}$$ And the relationship to force is $$F=-\frac{dU}{dr}$$ In electrostatics we instead talk about electric field and electric ...
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Does magnitude of a charge influence magnitude of force that individual charge exerts on another charge [closed]

two point charges, q1 and q2, are placed 0.3m apart on the x-axis, as shown in the figure above. Charge q1 has a value of -3 nano Coulomb and q2 has a value of +4.8 x10^-8 C. The net electric field ...
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Is a given charge density a surface charge density or volume charge density?

The exact question goes like this: In a certain electronic tube, electrons are emitted from a hot plane metal surface, and collected by a plane metal plane parallel to the emitter, at a distance ...
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1answer
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Image charge method to find electric field [closed]

The following is a question from my tutorial on boundary value problems and image charge method- A point charge +q is placed at (0, 0, d) above a grounded infinite conducting plane defined by z = 0. ...
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1answer
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Electrostatic Potential Energy Integral

I'm trying to calculate the total energy of a simple two charge system through the integral for electrostatic energy of a system given in Griffiths' book: $$U = \frac{\epsilon_0}{2}\int_V E^2 dV .$$ ...
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3answers
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Is there a place on the equipotential surface where a charge feels no electric force? [closed]

I'm given a graph of an equipotential surface where I need to find a place where a charge feels no electric force. I feel like it will be where the voltage is zero, which would be 2G on the graph, ...
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1answer
78 views

Why isn't the electric field just a mathematical tool?

I'm limiting my question to this field because it is the only one I know of with a certain degree of knowledge. I doubt they really exist because of the following reasoning: Coulombs law was stated ...
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Conductors and Uniqueness Theorem

I'm working with Griffiths Electrodynamics, and he introduces a uniqueness theorem: First Uniqueness Theorem: The potential $V$ in a volume $\Omega$ is uniquely determined if (a) the charge ...
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1answer
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Using Maximum Principle to see conductor is equipotential

This is a problem from electrostatics, but I'm trying to understand it in terms of harmonic functions. Let $B\subset\mathbb{R^3}$ be a conductor. It can be shown that the electric potential ...
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Curvature of electrostatic potential is zero

Could you please expound upon this claim? I found such claim on Zangwill's Classical Electrodynamics, which states that constraint coming from Laplacian equation implies electrostatic potential has ...
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Why is the shape of lightning or an electric spark a zig-zag line?

Why is the shape of the lightning (or an electric spark) always of a zig-zag nature? Why is it never just a straight line? Image source.