Negative Voltage when Magnet Falls Through Solenoid: Gaining Energy?

[Miraj Kayastha]

when a magnet is falling through a solenoid, voltage is produced.
Once positive is produced and the when the magnet leaves the solenoid negative voltage is produced.

Voltage is the energy lost by a unit charge when traveling from one point to the other.

So if there is negative voltage produced, does this mean charge gains energy?

 

[Born2bwire]

Voltage requires a defined path (though because the electric field is a conservative force, the actual path does not matter, only the endpoints). So yes, if you have a negative voltage, then a test charge would gain energy by following that path. Reverse the path and you have a positive voltage which is the energy you have to expend to move the test charge back to the starting position.

EDIT: Should qualify that the sign of your test charge matters too. We are talking about a positive charge above. A negative charge would be the opposite.

 

[willem2]

Whatever the sign of the voltage, and whatever the sign of the charge of the test charge, the field will make it move in a way that it gains kinetic energy from the field. It's dangerous to talk about potential energy, because the electric field is not conservative in the presence of a changing magnetic field.
If you hook up a resistor to the solenoid, it will produce heat, both with a negative and a positive voltage across it.