# Is Electric Field Not a Conservative Field When it's Produced by Change of Magnetic Field?

The condition for a field $\vec{E}$ to be conservative is: $\nabla \times \vec{E}=\vec{0}$. In electrostatics, $\nabla \times \vec{E}=\vec{0}$ is followed strictly, but Faraday's law says that: $$\nabla \times \vec{E}=-\frac{\partial}{\partial t}\vec{B}$$ Does this mean when $\frac{\partial}{\partial t}\vec{B}\neq\vec{0}$, the electric field is not conservative?

• yes, the definition of a conservative vector field V is $\nabla \times \textbf{V} = 0$ therefore if $\nabla \times \textbf{V} \neq 0$ the field is non conservative – tomph Jan 9 '17 at 11:02
• – Qmechanic Jan 9 '17 at 11:40