When a current flows through wire, it sets up a magnetic field in a direction determined by the right hand rule. This means that if you places your finger around the wire, pointing in the direction of the current, your thumb would point in the direction of the magnetic field.

Lenz's Law states that if there is a change in the magnetic field inside of a loop of wire, then a current will form in the wire. Furthermore, the direction of the current will be such that the magnetic field it creates opposes the direction of change in the magnetic field. Look closely and notice that the current induced sets up a magnetic field consistent with the right hand rule.

Here we examine a different method of changing the magnetic field inside a loop of wire. The yellow is a region of constant magnetic field (into the screen). When we move the loop across this region, since the area affected by the magnetic field changes, the loop senses a changing magnetic field. This has the same result as above, and a current is induced in the loop. Notice here that when the loop is completely outside or inside this region of constant magnetic field, there is no current.

Eddy currents are the result of Lenz's Law when applied to a large chunk of a conductor. When a chunk of conductor is moved through a magnetic field, many loops of current (one is depicted here) are set up in the conductor. These are known as Eddy Currents. This will usually cause the conductor to heat up; so this phenomenon is utilized in induction stoves. Another application of eddy currents is in superconductors.

When some materials are cooled below a critical temperature, they become perfect conductors, called superconductors. Then the magnetic field inside them vanishes, regardless of any external field.

When a superconductor (the black slab) is placed near a magnet (the metallic cylinder), eddy currents are induced in the superconductor in such a way that a magnetic field is set up outside the superconductor which exactly cancels the external magnetic field. The net result is two opposite poles of a magnet. This can be realized in that when you place a small magnet above a superconductor, the small magnet levitates.