Moving Magnets, Magnetic Fields, Currents and Coils
A changing magnetic field induces a current and a changing current induces a changing magnetic field. This is used in transformers to change high voltages to low voltages or vice versa. You don't need a changing current to induce a magnetic field however. A current will exist around a current carrying a constant current according to the Right Hand Grip Rule.
It is stated above that a changing magnetic field induces a current. A changing magnetic field may be produced in two ways: if a magnet is moving close to a loop of wire - note that if the magnet or direction of motion of the magnet is reversed, the direction of the current will be reversed too,
or if a current in a loop is changing. In either case if there is a loop of wire present there will be a current induced in that loop of wire BECAUSE OF THE CHANGING MAGNETIC FIELD. The link with a changing magnetic field may be harder to understand. It arises because a current loop generates a magnetic field.
If the strength of the field changes, because for example, the current increases or decreases, then a current may be induced in any nearby loop.