Which statment forms the basis of faraday's law of induction?
a changing magnetic flux establishes a current in a circuit.
a currnet flowing through a wire establishes a magnetic field
the magnetic moment of a conductiong loop carrying current depends on the area of the loop
a permanent magnet creates a magnetic field at all points in the surrounding space

A changing magnetic flux establishes a current in a circuit.

Faraday's Law of Electromagnetic Induction was formulated from the experiments made by him and states that:  

The voltage induced in a closed circuit is directly proportional to the speed with which the magnetic flux that crosses any surface with the circuit as edge changes in time

where:  

is the Electric Field  

is the infinitesimal element of the C contour

is the magnetic field density

is an arbitrary surface, whose edge is C  

The negative sign indicates the direction of the induced current and refers to the opposition between the fields induced by the magnetic flux and the electromotive force.  

So, it is the change in the magnetic flux that establishes a voltage in the circuit, hence current.

b.a device that inputs heat into a cool object

the minimum amperage that the current in this wire would have to have so that its weight is completely supported by the magnetic force due to earth's field, assuming that no other forces except gravity act on it