Calculating the energy transferred?

1. Dash-IQ

108
A conductor is placed in a magnetic field.
When a power source connected to the conductor creates a voltage difference in a conductor, current starts to flow.

Now the conductor gains KE due to the Lorentz force being applied, I want to calculate the energy transferred from the power source to do this work, is E = P x t a good formula?
Should I consider the change in time for power to stabilize although its a extremely fast process?