Question

. Show that a uniform electric field cannot exist in the presence of a time-dependent magnetic field.

Answer 1

For a uniform electric field, $\text{curl }\vec E=0.$

But, according to Maxwell–Faraday equation, for a time-dependent magnetic field, we have that

$$\text{curl }\vec E=\dfrac{-\partial \vec B(t)}{\partial t}\not=0.$$

That is why a uniform electric field cannot exist in the presence of a time-dependent magnetic field.