GG 652: Homework 5
Magnetization
Reading: Blakeley Ch. 5 Due: Thursday 7 February 2013
1) Problem 1, p. 98: Use Poisson’s relation to find the magnetic field inside as well as outside a uniformly
magnetized spherical shell.
2) Problem 2, p. 98. i.e., What nonzero distribution of magnetization within a spherical surface produces no
magnetic field (i.e., what is the magnetic annihilator for a spherical source)?
3) A spherical cavity of radius a is buried with its center at a depth a within a layer of earth that is vertically
and homogeneously magnetized. The layer has a thickness t > 2a and magnetization M=M k̂ .
(a) Find an expression for B in terms of M at any point on the surface above the cavity.
(b) What is B directly over the center of the cavity? How does the magnitude at this location depend on a?
4) As new oceanic crust is formed at a mid-ocean ridge, it becomes permanently magnetized parallel to the
Earth’s magnetic field. The Earth’s magnetic field has switched polarities from time to time (at times in the
past, it pointed south instead of north ). Therefore, long strips of seafloor become magnetized in alternating
directions and record isochrons of oceanic crust created through geologic time. In the equatorial Pacific the
seafloor is being created by the East-Pacific Rise (EPR) and the Galapagos Spreading Center (GSC). Crust
generated at the EPR has magnetized strips elongated in the north-south direction and crust generated at the
GSC has magnetic lineations oriented in the east-west direction (see diagram below). You can approximate
the lineations as being infinitely long in one direction.
To detect magnetic field variations you tow your magnetometer on two straight profiles. Profile 1 is
over seafloor generated by the EPR, profile 2 is over seafloor generated by the GSC.
(a) In which direction should you run each profile to obtain the largest signal of variation?
(b) Would you expect to measure larger variations over Profile 1 (EPR crust) or Profile 2 (GSC crust)?
(d) It is typically the variation in the total field strength (i.e., that of the Earth’s main field plus the local
anomalous field due to the crust) that is measured. Since the Earth’s field is mostly horizontal near the
equator your magnetometer will be primarily sensitive to the horizontal component of the anomalous field.
Sketch how you might expect the horizontal component of the field to vary along the profile identified in (b).
Note, the magnetic lineations are much wider (tens of km) than they are deep (~3 km).