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### The Normal Derivative Of Electric Field

Monday, July 4th, 2011

By Euprime B. Regalado From Gauss theorem, we can show that the surface of a curved charged conductor, the normal derivative of the electric field is given by where and are the principal radii of curvature of the surface.  Gauss’s law in integral form is expressed as when there are no charges enclosed in the […]

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### Proving properties of electric fields using Gauss’s Theorem

Monday, July 4th, 2011

Author: CHRISTINE ADELLE L. RICO Use Gauss’s theorem and to prove the following: (a) Any excess charge placed on a conductor must lie entirely on its surface. (A conductor by definition contains charges capable of moving freely under the action of applied electric fields.) Solution: Suppose that the field were initially nonzero. Since this is […]

### Vector Analysis

Wednesday, June 29th, 2011

Prove: where:     Sol’n:   then:             or

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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,

### 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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