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Solving for the electric field using Gauss’ theorem

Monday, July 4th, 2011

Bianca Rae B. Sambo Problem 1.4 (Classical Electrodynamics, 3rd Edition by Jackson)   Each of the three charged spheres of radius a has a total charge Q. One is conducting, one has a uniform charge density within its volume and one having a spherically symmetric charge density that varies radially as where (r>-3). Use Gauss’ […]

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Prove Green’s Reciprocation Theorem

Monday, July 4th, 2011

Author: Kayrol Ann B. Vacalares MS-Physics 1, MSU-Iligan Institute of Technology ______________________________________________________________   Prove Green’s Reciprocation Theorem: If is the potential due to a volume-charge density within a volume V and a surface charge density on the  conducting surface S bounding the volume V, while is the potential due to another charge distribution and , […]

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Proving Vector Identity Using Levi-Civita Symbol

Tuesday, June 28th, 2011

Roel N. Baybayon MSPhysics1 ————————————————————————————————– We are going to prove the following vector identity using Levi-Civita symbol: Solution: Let    ,     ,   ,   . Then, By definition: We have to let m=n so that, Levi-Civita symbol can be expressed in terms of Kronecker delta given by: Thus,    

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Verifying vector formulas using Levi-Civita: (Divergence & Curl of normal unit vector n)

Tuesday, June 28th, 2011

By Sim P. Bantayan, MS Physics I, MSU-IIT Let , and where and .   1. Prove that . Proof: Now, . Since i=j for the divergence of normal unit vector n, but (i=j). Moreover, for three dimensions, , so Therefore, .   2. Prove that . Proof: . Since i=j for the curl of normal unit vector n, […]

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Prove that the Divergence of a Curl is Zero by using Levi Civita

Tuesday, June 28th, 2011

Author: Kayrol Ann B. Vacalares The divergence of a curl is always zero and we can prove this by using Levi-Civita symbol. The Levi-Civita symbol, also called the permutation symbol or alternating symbol, is a mathematical symbol used in particular in tensor calculus. Prove that: = 0 Proof: Let: and To show that:  = 0 First,       Here are the possible […]

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