of induction gives: \nabla \times \mathbf{E} = -\dfrac{\partial \mathbf{B}} {\partial t} = 0 \nabla \times is the curl operator . t is time. Since the curl of the electric field is zero, it is defined by a scalar electric potential field, \varphi (see Helmholtz decomposition ). \mathbf{E} = -\nabla \varphi Eliminating