Work done by power supply to maintain a constant current

[mymodded]

Homework Statement

A coil with N turns and area A, carrying a constant current, i, flips in an external magnetic field, ##\overrightarrow{B_{ext}}##, so that its dipole moment switches from opposition to the field to alignment with the field. During this process, induction produces a potential difference that tends to reduce the current in the coil. Calculate the work done by the coil's power supply to maintain the constant current.

Relevant Equations

$$U = NiAB\sin(\Theta)$$

Since we want the current to stay constant, the change in potential energy that's caused by the coil flipping in the magnetic field should be "undone" by the work done by the power supply, so shouldn't ##W = -\Delta U## ? the answer guide did it without the negative sign, so I'm wondering if the negative sign should be included or not and because we don't really want to add more potential energy.