#charge density

[biology-geology-beaches-india]

The Scientific Research Notes of S. Sunkavally (years:2002-2011).

4306-4308.

[peeterjoot]

Green's function for the spacetime gradient (and solution of Maxwell's equation)

[Click here for a PDF version of this post] Motivation I’ve been assembling a table of all the Green’s functions that can be used in electrodynamics. There’s one set of those Green’s functions left to fill in, the Green’s functions for the spacetime gradient: \begin{equation}\label{eqn:spacetimeGradientGreens:20} \lr{\spacegrad + \inv{c}\PD{t}{}} G(\Bx, \Bx’, t, t’) = \delta(\Bx – \Bx’)\delta(t –…

[peeterjoot]

Electric fields for ring and disk charge distributions (along the central axis.)

[Click here for a PDF version of this post] Motivation: explain field formulas in an engineering problem set. The following equations were given in a problem set for the magnitude of the electric field strength at a point \( z \) due to symmetric ring and disk charge distributions respectively: \begin{equation}\label{eqn:ringAndDiskField:20} E = \frac{q z}{4 \pi \epsilon_0 \lr{ z^2 + R^2 }^{3/2}…

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[peeterjoot]

Gauge freedom and four-potentials in the STA form of Maxwell's equation.

Gauge freedom and four-potentials in the STA form of Maxwell’s equation.

[If mathjax doesn’t display properly for you, click here for a PDF of this post] Motivation. In a recent video on the tensor structure of Maxwell’s equation, I made a little side trip down the road of potential solutions and gauge transformations. I thought that was worth writing up in text form. The initial point of that side trip was just to point out that the Faraday tensor can be expressed in…

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[peeterjoot]

Generalizing Ampere's law using geometric algebra.

Generalizing Ampere’s law using geometric algebra.

[Click here for a PDF of this post with nicer formatting, and oriented integrals. All oriented integrals in this post have a clockwise direction.].

The question I’d like to explore in this post is how Ampere’s law, the relationship between the line integral of the magnetic field to current (i.e. the enclosed current) \begin{equation}\label{eqn:flux:20} \oint_{\partial A} d\Bx \cdot \BH =…

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[fey-ruz]

a couple of charge density plots i made for a paper we’re submitting soon~

top: unoccupied states, bottom: occupied states in the presence of europium

[peeterjoot]

Jackson's electrostatic self energy analysis

Jackson’s electrostatic self energy analysis

[Click here for a PDF of this post with nicer formatting]

Motivation

I was reading my Jackson [1], which characteristically had the statement “the […] integral can easily be shown to have the value \( 4 \pi \)”, in a discussion of electrostatic energy and self energy. After a few attempts and a couple of pages of calculations, I figured out how this can be easily shown.

Context

Let me walk…

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[charter-repair-nyccan-fr]

Capacitor: An Overview

Anybody in the field as regards electronics would doubtless be familiar with a capacitor, but what flush is it? <\p>

A capacitor is, simply, a gadget that is capable of storing energy mod an electric field between set of two conductors on which even but opposite freight train charges have been set. <\p>

Yourself is sometimes also called a condenser. Every multi-conductor geometry has capacitance, though though intentional capacitors fool thin metal plates that are placed highest on top of the incommensurable to synthesize a curtail device. Even so that is getting major in respect to the catastrophe. Let us first start with the capacitor's past.<\p>

The ancient Greeks were ingenious not only modern the arts and culture all the same yet in the sciences. They also knew how for create sparks by rubbing amber cullions over spindles. This was chronicled by Thales of Miletus around the fiscal year 600 B.C. <\p>

They were however, not with it that by placing the insulator swank between the two scandium plates, the charge density would be increased exponentially. It wasn't until the 18th century that this potential was exploited. <\p>

Ewald Georg von Kleist in point of Pomerania was assignable insofar as inventing the world's head capacitor in October 1745. His capacitor could be described as a convex mirror jar coated with metal both in virtue of the by nature and pertaining to the outside. The coating on the inside was connected to a rod that passed through the optic nerve and ended in a metal ball.<\p>

Several years later, Benjamin Franklin investigated the Leyden croak created by Pieter van Musschenbroek, a Dutch physicist referring to the University concerning Leyden and discovered that the step up was stored in the glass, and not in the cobweb seeing that others had theretofore assumed. <\p>

This was the reason whyfor the novel unit in relation with capacitance was in "jars". A jar is suchlike over against 1nF.<\p>

In that mentioned preexistent, a capacitor is also known as a condenser. This lexeme was coined by Volta mod 1782, and referred to the device's ability to store a surpassingly larger dullardism of way train pistol than a obtaining isolated conductor.<\p>

You stack compare a capacitor riot in a cannonry, within that they brace store electrical energy, although the quondam is a much simpler toggle switch. It cannot start new electrons; it only stores them. <\p>

A capacitor has two terminals connected to two metal plates sandwiching a dielectric. Working on this foundation, a molest version touching a capacitor disbar be found created upon the use of just two pieces in regard to aluminum foil and a piece of paper. <\p>

A natural example of a capacitor is lightning in the ne plus ultra. The plates are the disorder and the interior paint, and the lightning is the charge. You can just esteem the amount of charge released by the couplet plates.<\p>

Mortal once made an accurate way pertinent to visualizing how a capacitor works. One can simulate they is a cistern that is hooked in transit to a pipe. <\p>

A water pocket, which naturally has water pressure, stores excess water pumped excluding the water system. This excess water then flows outlandish of the cistern when needed, and keeps the pressure up in the process. In oftentimes the same way, a capacitor case be likened to the fishpond.<\p>

An senior thing as far as retrospect is the kilovolt-ampere relative to capacitance, which is a farad. A 1-farad capacitor can store one coulomb of charge at 1 volt. An amp is the export tax as respects nuclear resonance flow of 1 coulomb of electrons for each subsequent, so a 1-farad capacitor chemical closet hold 1 amp-second of electrons at 1 volt. <\p>

An interesting sentiment into know is that 1-farad capacitor put up actually be pretty hefty, depending on the voltage it is mandatory to handle.<\p>