Question

if you approximate the earth’s magnetic field as the field of a magnetic dipole, the field will decrease roughly as 1/r3 , just as for an electric dipole field. the magnetic field is 0.50×10⁻⁴ t at the earth’s surface.

Answer 1

The Earth's magnetic field can be approximated by a magnetic dipole's field, which decreases rapidly as 1/r³, consistent with the observed decrease in strength away from a bar magnet.

Step-by-step explanation:

The student's question deals with the approximation of the Earth's magnetic field as that of a magnetic dipole and its change with distance from the center of the Earth. At the Earth's surface, the magnetic field is given as 0.50×10⁻⁴ T.

We know that a magnetic dipole's field decreases roughly as 1/r³, where r is the distance from the dipole. Thus, as one moves away from the Earth's surface or the magnet, the magnetic field's strength decreases rapidly, similar to the decrease in strength with distance for an electric dipole field. This is consistent with observations of bar magnets, where the field is strongest close to the poles and weakens with distance. The Earth's magnetic field strength slightly less than 5×10⁻⁵ T at the surface is therefore consistent with the field of a magnetic dipole.

Additionally, as per the reference information, a magnetic dipole placed in a magnetic field will tend to align itself with the magnetic field vector, and the strength of the magnetic field is greater where its lines are denser, which is coherent with the experience and properties of bar magnets.