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## Archive for the 'Quantum Science Philippines' Category

### Solving for the distribution of charge where time-averaged potential is given

Monday, July 4th, 2011

by Sim P. Bantayan, MSPhysics I, MSU-IIT   Problem 1.5 The time-averaged potential of a neutral hydrogen atom is given by where q is the magnitude of the electronic charge, and being the Bohr radius. Find the distribution of charge( both continuous and discrete) that will give this potential and interpret your result physically.   […]

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### Mean Value Theorem (Classical Electrodynamics)

Monday, July 4th, 2011

Roel N. Baybayon MSPhysics1-MSU-IIT ————————————————————————————— Problem 1.10 Prove the mean value theorem: For charge-free space the value of the electrostatic potential at any point is equal to the average of the potential over the surface of any sphere centered on that point.   Proof: To prove this problem, we are going to use the Green’s  […]

### 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 […]

### 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 […]

### 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 . […]