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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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Electrostatic Energy and Energy Densities of Different Capacitors

Monday, July 4th, 2011

Electrostatic Energy and Energy Densities of Different Capacitors Author: Quennie J. Paylaga, Master of Science in Physics student Problem 1.8 (Chapter 1 of Classical Electrodynamics 3rd Edition by JD Jackson) Calculate the electrostatic energy (express it in terms of equal and opposite charges Q and -Q placed on the conductors and the potential difference between […]

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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 […]

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Curl of the product of a scalar and a vector using Levi-Civita

Friday, July 1st, 2011

By Eliezer Estrecho To prove this formula, we use the following: Where: and Using the equation above: We can factor out in the first term to give: Note that for the second term, the permutation of indices are odd, rearranging them to ijk will give the negative: Thus, About the author: Eliezer Estrecho is currently […]

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Proving Vector Identity Involving the Unit Vector Using the Levi-Civita and the Kronecker Delta

Wednesday, June 29th, 2011

*author: Michelle R. Fudot   Prove: ___________________________________________________________ Proof: First, we define the following vectors as: ; ; and Now,  if we let i=k, then . Furthermore, Now, the derivative of orthonormal basis , that is, and the derivative of a coordinate X, . Also, , thus = = = = It is noted that . […]

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