From where is energy got in electromagnetic induction? I've been reading about electromagnetic induction and while the concept of transfering energy via magnetic field is intuitive, what I'm confused about is, where is the current or energy got from? I know that the electromagnetic force is defined as
$$e = -\frac{d}{dt} \Phi$$
where $e$ is the resulting electromagnetic force and $\Phi$ is the magnetic flux of the magnet.
But from where is the energy got and does it follow the law of conservation of energy ? Or can induction be used to create "infinite" amounts of energy?
 A: The answer is in the application of Lenz's law.
An emf is induced and if there is a complete electrical circuit an induced current flows in such a direction as to the motion producing the induced current (emf).
For example suppose that you have the north pole of a magnet approaching a coil which is connected to a resistor.
Because there is a changing magnetic flux linked with the coil an emf is induced in the coil and so there will be an induced current in the circuit.
The direction of the induced current will be such as to induce a north pole at the end of the coil towards which the north pole of the magnet is travelling.  
So whatever is moving the magnet will have to do work to push the magnet towards the coil as the two north poles repel one another.
It is that work which is done pushing the magnet which is the source of the electrical energy used to drive the induced current around the circuit.
If it had been a south pole which had been induced then no work would be needed to move the north pole of the magnet towards the coil and yet a current would be flowing producing heat in the circuit.
This would contradict the law of conservation of energy and so it is a north pole which is used to induce the current and not a south pole. 
A: Im afraid the energy has to come from somewhere otherwise we have created an impossible machine.
Induction requires an alternating magnetic field to be generated in the first place. This takes energy. In fact, more energy than you get out from the induced current in the field.
A transformer (as you would find in a phone charger) consists of a primary coil that is powered by the mains electricity. Closely connected to it via a nice metal core is a secondary coil. 
The primary takes alternating current from the mains and creates an alternating magnetic field. 
The secondary is in the alternating magnetic field and an induced current is created in it. (The current to your phone is rectified in the transformer to DC)
Older types will become warm. Why? Because the primary coil creates an induced current in the core too. Thats why when you take one apart you will see the core is made of multiple leaves of metal that is an attempt to reduce the induced currents in the core. It is these that contribute to the transformer's inefficiency.
