Regenerative magnetic braking system
What you have designed is a generator that dissipates the power it converts from the mechanical energy in-place.  That is largely irrelevant to a design that transmits the converted energy to elsewhere over electrical wires.

So basically, ditch your current design and start over, this time designing to the actual specs.

There are many types of generators and options out there.  You want something that looks like some type of DC motor run in reverse.  Most DC motors work pretty well backwards as generators too.  In fact, in electric cars, the same unit works as the motor to push the car forwards, and as the generator to put mechanical load on the wheels to perform regenerative breaking.