Maxwell's equations (Ampere's law and Faraday's Law) say that:
Del. X E = - partial B/partial t.$$\nabla \times \vec{E} = - \frac{\partial B}{\partial t}$$
To me, the derivative on the LHS is a spatial one, the partial on the RHS is a time varying one. So all we can deduce from this is that a time varying magnetic field generates a curly E field (says nothing about time varying E field). So why do textbooks typically make the statement that time varying E field produces a time varying B field ?
