Why is high open loop gain needed for an Op-Amps virtual ground?

Question

In books, I often see that they state that the op-amp has a virtual ground property when it has a high open-loop gain and in a negative feedback configuration.

First Question: The negative feedback part makes sense to me, but why is it necessary to have a high open loop gain to satisfy the virtual ground property?

Second Question: How does steady-state error from control theory tie into op-amps? Increasing open-loop gain improves the error? I'm trying to make a link between the two courses.

Answer 1

Scenarios 1 and 2 below apply when the op-amp is either open-loop or closed-loop: -

1. If the open-loop voltage gain is only 100 (for instance) then the voltage difference between the two op-amp inputs needs to be 10 mV to produce 1 volt at the output. 100 mV is needed to produce 10 volts at the output.
2. If the open-loop voltage gain is 10,000 then the the voltage difference between the two op-amp inputs need only be 0.1 mV to produce 1 volt at the output. 1 mV is needed to produce 10 volts at the output.

In the second scenario, the difference between the op-amp inputs is mainly less than 1 mV and you would say that this is much more of a virtual earth/ground than the first scenario. And for many op-amps (at DC), the open-loop voltage gain is in the order of 100,000 to 1,000,000.

How does steady-state error from control theory tie into op-amps? Increasing open-loop gain improves the error? I'm trying to make a link between the two courses.

An op-amp is a control system and so it applies 100%.