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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 . […]

Posted in Electrodynamics, Quantum Science Philippines | No Comments »

Curl of the Gradient of a Scalar

Wednesday, June 29th, 2011

proof that the curl of the gradient of a scalar function is equal to zero let and

Posted in Electrodynamics | No Comments »

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, […]

Posted in Electrodynamics | No Comments »

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 […]

Posted in Electrodynamics | 3 Comments »

Verifying a Vector Identity (BAC-CAB) using Levi-Civita

Monday, June 27th, 2011

Author: CHRISTINE ADELLE L. RICO Here is another method of verifying a vector formula using the Levi-Civita symbol. Levi-Civita symbol is a tensor of rank three and is defined by +1 if the indices are in even permutation of , -1 if the indices are in odd permutation, and 0 if any two indices are […]

Posted in Electrodynamics | 1 Comment »