Final answer:
The precise force on one of two closed current-carrying loops due to the other depends on their relative orientation and distance, which are not specified in the question. To calculate such forces, one must apply laws like Biot-Savart or Ampere's Law, considering the currents and resultant magnetic fields.
Step-by-step explanation:
The general expression for the force on one closed loop due to another involves the magnetic fields and currents in both loops. When calculating the force between two circular loops of radius R, one in the XY plane and another in the YZ plane, both sharing the same center at the origin, we must consider the complex interactions due to the magnetic fields produced by the currents in the loops. However, the exact force depends on the specific orientation and distance between the loops, which is not provided in the question. Generally, the magnetic field produced by a current-carrying loop can be determined using Biot-Savart's Law or Ampere's Law.
In scenarios where magnetic fields and forces need to be calculated, such as determining the magnetic force on current-carrying loops, it is crucial to consider the direction and magnitude of the currents, as well as the resulting magnetic fields produced by them. For example, the force on a loop in a uniform magnetic field can be calculated by summing the forces on each segment of the loop, as per the Lorentz force law, which states that the force on a current element is I dl × B.