# How is energy/momentum conserved in a simple generator?

If we consider a simple generator of electricity a bar magnet (solenoid) passing through a solenoid conducting wire. Using the right hand rule and left hand rule you can see roughly that the direction of current passing through the conductor is the same as the current creating the bar magnet. Further use of the left hand rule tells me that the force on the magnet is applied in the normal direction to the solenoid rings.

So what is happening, how is energy being converted. Where is momentum going? The problem is, I want to be able to show that momentum and energy is conserved even in magnetic induction. But how can I when the forces always act perpendicular to the fields? It doesn't seem to work

Imagine that you had the solenoid on a frictionless truck which could move in the horizontal direction.
The solenoid is at rest and you shoot a magnet, north pole first, into the solenoid.
Ignoring friction the magnet would induce an emf in the solenoid but if no current flowed in the solenoid the magnet would pass through the solenoid without changing its velocity.
If the ends of the solenoid are connected together the an induced current would flow in a direction such as to oppose the change producing it - Lenz.
Due to the induced current a north pole will be induced at the end closest to the incoming north pole of the magnet.
The solenoid on the truck would begin to move, gaining momentum and kinetic energy and the magnet would be losing momentum and kinetic energy.

You could imagine a situation where the magnet stops moving relative to the solenoid and so there is no more induced emf or induced current.
The total momentum of the solenoid, truck and magnet would be equal to the initial momentum of the magnet.
The kinetic energy of the solenoid, truck and magnet would be less that the initial kinetic energy of the magnet.
The difference is the heat generated in the solenoid when there was an induced current.

What you have is an inelastic collision (interaction) between the solenoid and the truck, and the maagnet.

• ok, so they conserve linear momentum. But what about the initial force which created angular momentum in the electrons in the solenoid? How is angular momentum conserved? The induced magnetic field pushes electrons spinning in the magnet itself radially inwards. I cannot find a way to generalise conservation to any situation – lucky-guess Mar 27 '17 at 13:19
• I would suggest that the truck holding the solenoid would try and rotate in the opposite direction? – Farcher Mar 27 '17 at 13:36