Variational principle in 3D magnetostatic field

It is demonstrated that in a 3-D nonlinear field the variational principle does not hold. Using a dyadic operator, a new expression is introduced in place of the curl curl operation for vector potential translation of magnetostatic field equations. The control equation, taking the gauge of the vector potential A into account, is then clarified and found to be different from the equation in the linear medium. It is shown that the equation derived from the variational principle does not agree with the control equation in the 3-D nonlinear field, so the variational principle does not hold, and Ritz´s method can not be used. The variational principle in the 2-D field, is discussed