Question

You are a planetary geophysicist, studying the magnetic fields of other planets. From your studies, you have learned that Jupiter has the strongest magnetic field of any other planet in the solar system. Jupiter is also the largest planet in the solar system with a radius 69,910 km. Studies of its magnetic field show that the field is a dipole, and that at the equator it has a strength of 4.28X10-4 T. Given this information, determine;

2) The field strength at its closest moon, Io, which has an orbital radius around Jupiter of 4.22X10⁵ Km. Assume that jupiter's magnetic and field strengths are aligned, and that Io orbits around the equator.

Answer 1

The magnetic field of magnetic dipole m in the plane perpendicular to the axis of dipole and passing through the dipole is given by

where r is the distance of the point from the dipole.

RHS of the above equation is a constant for a dipole. We have

The point where the field is given and the point where the field is asked lies in the plane perpendicular to the axis of the dipole and passing through the dipole. So, the magnetic field and distance from dipole for these points are related as:

Using we get