Solution:

Assertion (A) is false: When a battery is supplying power (discharging), positive charge moves from the negative terminal to the positive terminal inside the battery, driven by non-electrostatic (chemical) forces. The internal electrostatic field points from the positive terminal to the negative terminal. Thus, the electrostatic force on positive ions opposes their motion, doing negative work.

Reason (R) is also considered false in this context: While the *electrostatic* field due to charge separation points from positive to negative, the effective field that *drives* the current (the non-conservative EMF field) is directed from the negative to the positive electrode. If 'Electric field' in (R) implies the driving force for current, then (R) is false. Therefore, both (A) and (R) are false.