I wanted to ask under what conditions will charges not flow in a closed circuit. Or when is current through the circuit zero even when an EMF is applied? Like in the case of potentiometer, we say that we are measuring the emf of the battery because current through the secondary circuit is 0? So what condition are we fulfilling here so that current is 0?
Basically, it is infinite resistance; consider Ohm's law
$$ I = V/R $$
if you let $R$ get arbitrarily large, then the current goes to zero.
Current is zero every time resistance tends to zero [ because infinite resistance will be ofcource a open circuit.
like in case of a capacitor , after long time the current is zero because all the potential is dropped about the capacitor and current is zero.
In case on potentiometer current does not flow in secondary circuit is true because when balance point is achieved the potential drop across both wires is same , no driving force for electrons is present inside the wireand (potentials apply equal and opposite drift on electrons) thus galvanometer show zero deflection.