# [Physics] Ampere’s circuital law and the type of surface to be used

electromagnetism

What kind of a surface can we use for Ampere's circuital law?
I was taught that any enclosed surface can be used for Gauss's Law(something like a cube,a sphere)-essentially 3-D enclosed surfaces.

For Ampere's law, I have used a circular ring for calculation of Magnetic field due to wire(and also rectangular shapes for solenoids)-essentially 2-D enclosed surfaces like a ring,rectangle etc.

Now when I came to know about Maxwell's Displacement Current, the book uses a bucket kind of a shape like in the figure.

I am confused.One side is open and the other is closed.(I apologize if this sounds dumb.I only have a basic idea about the law.I don't really understand the 'surface integral' part and how it's supposed to be used.)

I've seen this link.I don't understand what is said there.

This is because the electric field will only be present between the plates and if you choose the surface to be at right angles to the electric field, and hence the rate of change of electric field, then the integral will become $\mu_o \epsilon_o \frac {dE}{dt}A$ where A is the area of a capacitor plate.
$E=\frac {q}{\epsilon_o A}$ so the integral is $\mu_o I$ because $\frac{dq}{dt}=I$ which makes it the "more familiar" right hand side of Ampere's law