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.
To show that:
Here are the possible values of :
if i,j,k is cyclic and non-repeating.
if i,j,k is anti-cyclic or counterclockwise.
if there are any repeated index.
Consider i,j,k to be cyclic and non-repeating, so
But if i is not equal to j
and if i= k
Since i,j,k is non-repeating and , therefore