Is there a magnetic field between capacitor plates while the capacitor is charging?

(Edit, Question was previously: "Can a changing electric field produce a magnetic field?")

I've just began studying Maxwell's equations today and what really had my attention is Ampere's law, the second term in particular. $$\int\vec B \cdot d\vec l=μ_0I_{encl}+μ_0ε_0\frac{dΦ_E}{dt}$$ Does this mean that a changing electric field can cause a magnetic field? For example, during the charging of a capacitor, between the plates where the electric field is changing.

I saw an exercise example where we changed the voltage across a capacitor and thus created a magnetic field.But some websites state that as long as there is no current - charge movement , there is no magnetic field being created. I read the same about the capacitor in particular. Could the example be wrong or is there a difference ?