Magnetic field inside parallel plate capacitor

Question

Inside a parallel plate capacitor, we know that the electric field due to the static charge $E= \frac{\epsilon_0 A}{d} $ Now if we want to find the magnetic field inside the parallel plate capacitor, wouldn't we get zero due to the Ampere's law?

Actually I want to ask that, when do I have to consider the Maxwell's correction to the amperes law?

If we consider the maxwells correction, we get, $$ \oint \vec{B}. \vec{dl} = \mu_0 \epsilon_0 \frac{d \phi_E}{dt} $$

How to calculate then the magnitude of B?

Answer 1

In the equation that you wrote(the correction) you must also add $μ_0I$. And you must ALWAYS consider both the time-changing electric field and the current I that penetrate the surface defined by your closed loop(from your line integral of $B\cdot dl$). You don't just choose when to consider $I$ and when to consider $\frac{dE}{dt}$. They both define this law, the Ampere-Maxwell law.
The only freedom that you do have is in what surface you can work with, because your closed loop defines an infinite number of surfaces(all with boundary defined by the line integral). So, sometimes you can make the smart choice and choose a surface to work with that makes your calculations easier(in some cases, some surfaces have only an $E(t)$ penetrating the surface while others-in the same problem- have only $I$ penetrating them).