In addition to what others have said, another interesting question to
ponder is why the airplane yaws when you bank.

The yaw is induced by the ailerons, so the only time you need to apply
rudder is when you are changing your bank angle with the ailerons. On
the side where the aileron is down, the wing has more lift, and more
drag. On the other side, the lift is spoiled and there is less drag.
The draggy wing yaws backwards, requiring opposite rudder.

This is why when you initiate a bank, you need to apply rudder in the
direction of the bank while the ailerons are in use, but not once you
stabilize the bank and neutralize the ailerons. When you roll back
wings level, you need to apply rudder the other direction to once
again compensate for the ailerons.

Dean