The magnetic fields of Earth and Jupiter originate from different places within the respective planets. Jupiter's field originates from a metallic, hydrogen core that spins rapidly, creating a powerful electrical current. Earth's core is molten iron but is not magnetic due to temperatures being so high as to neutralize magnetism. The electric currents that produce the magnetic field come from the rapid circulation of this molten iron core and not the metal itself.
The two planets are so different in size that the fields are obviously not the same. Comparing the two planets' field strengths at the top of their respective cloud covers, Jupiter's field is 10 times stronger than that of Earth. Jupiter's field extends more than 466 million miles from the planet's surface, whereas Earth's field reaches just 36,000 miles into space.
Both planets possess Van Allen Belts within their magnetic fields. These are areas in which large concentrations of charged particles have accumulated. The particles tend to have been emitted by the Sun and reach the belts via powerful solar winds. In the case of Earth, these particles cause the colorful aurora phenomenon. Around Jupiter, high rotational forces from the planet compress the particles into plasma sheets. The particles in these sheets bombard the moons of Jupiter, in turn creating more charged particles, which add to the belts. The particles and dust created from the moons form rings around Jupiter.
Jupiter and Earth both have colorful aurora phenomenons that are visible at the planetary magnetic poles. On Earth, the aurora is caused by charged particles carried into its atmosphere by solar winds. Jupiter's magnetic field is so vast and powerful, however, that the particles carried on solar winds are deflected long before they reach the planet's atmosphere. Even so, Jupiter has auroras, so the necessary particles must come from somewhere and it is likely that charged dust from the planet's eroding moons causes the phenomenon.