When a current is flowing in a wire a magnetic field is around the wire - as soon as it stops flowing the magnetic field disappears!

An electromagnet is a coil of wire (usually with a core in it - but the core is NOT the electromagnet the coil is the important bit!). When a current passes through the coil, the coil acts like a magnet - when no current flows there is no magnetic field.

The bigger the current, the stronger the field,

The greater the number of turns, the stronger the field

The stronger the field the closer the field lines - they are more densely packed.

The presence of a soft iron core increases the strength of the field substantially but the core must be soft iron otherwise when the current is switched off the core would still be magnetised.

Electromagnets are used in domestic and industrial devices, eg electric bells, lifting magnets, relays

Wires carrying an electric current produce a magnetic field with concentric circular field lines around them.

The current in a coil produces a magnetic field pattern similar to that of a bar magnet

The strength of an electromagnet is increased by the presence of a soft iron core because the domains in that core line up to reinforce the field produced by the coil of current carrying wire. The coil and the core have a magnetic field.