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’ [...]

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 , [...]

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,     Share and [...]

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, [...]

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 [...]