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Mass-Energy Equivalence

Thursday, November 5th, 2009

Overview of Mass-Energy Equivalence

Description

A detailed tutorial on mass-energy equivalence. Step by step tutorial including several examples of mass-energy equivalence for reference.

Overview

Mass-energy equivalence is the concept that the mass of a body is the measure of its energy content. This is often expressed by a formula written by Einstein, who is also the one that proposed the idea of mass-energy equivalence. This formula is $E = mc^2 \,\!$ , where E is energy, m is the mass, and c is the speed of light in a vacuum.

Tags: Albert, body, c, content, differential equations, E, Einstein, energy, equivalence, equivalent, formula, idea, light, m, mass, measure, speed, vacuum
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Maxwell’s Equations

Tuesday, September 22nd, 2009

How to Solve Maxwell’s Equations

Description

A detailed tutorial on the solving of Maxwell’s Equations. Step by step tutorial including several examples of how to solve Maxwell’s Equations for reference.

Overview

Maxwell’s equations are a set of four partial differential equations that describe the properties of electric and magnetic fields and relate them to their sources, charge density and current density. The result of these equations is that they show light is an electromagnetic wave. The four different equations and the way to express them is as follows:

Gauss’s Law: relates electric charge contained within a closed surface to the surrounding electrical field.

Differentiation: $\nabla \cdot \mathbf{D} = \rho_f$

Integration: $\iint_{\partial V}\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\;\;\;\subset\!\supset \mathbf D\;\cdot\mathrm{d}\mathbf A = Q_{f}(V)$

Gauss’s Law for Magnetism: states that the total magnetic flux through a closed surface is zero.

Differentiation: $\nabla \cdot \mathbf{B} = 0$

Integration: $\iint_{\partial V}\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\;\;\;\subset\!\supset \mathbf B\;\cdot\mathrm{d}\mathbf A = 0$

Maxwell-Faraday Equation: describes how a changing magnetic field can create an electric field.

Differentiation: $\nabla \times \mathbf{E} = -\frac{\partial \mathbf{B}} {\partial t}$

Integration: $\oint_{\partial S} \mathbf{E} \cdot \mathrm{d}\mathbf{l}� = - \frac {\partial \Phi_{B,S}}{\partial t}$

Ampere’s Circuital Law: states that magnetic fields can be generated by electrical current and changing electric fields.

Differentiation: $\nabla \times \mathbf{H} = \mathbf{J}_f + \frac{\partial \mathbf{D}} {\partial t}$

Integration: $\oint_{\partial S} \mathbf{H} \cdot \mathrm{d}\mathbf{l} = I_{f,S} + \frac {\partial \Phi_{D,S}}{\partial t}$

Tags: Ampere's Circuital Law, change density, closed surface, current density, density, electric charge, electric fields, electrical current, electromagnetic wave, Gauss's Law, Gauss's Law for Magnetism, Guassian surface, light, magnetic field, magnetic flux, Maxwell's equations, Maxwell-Faraday Equation, Physics, Science, zero
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Posts Tagged ‘light’

Mass-Energy Equivalence

Overview of Mass-Energy Equivalence

Maxwell’s Equations

How to Solve Maxwell’s Equations