Find the force of attraction between two magnetic dipoles,
_{}
and
_{},
oriented as shown in Figure 1, a distance *d* apart, using

(a) equation (6.2) of Griffiths.

(b) equation (6.3) of Griffiths.

(a) equation (6.2) of Griffiths.

(b) equation (6.3) of Griffiths.

A uniform current density
_{}
fills a slab straddling the *yz* plane, from *x* = -*a* to
*x* = +*a*. A magnetic dipole
_{}
is situated at the origin.

a) Find the force on the dipole using equation (6.3) of Griffiths.

b) Do the same for a dipole pointing in the*y*-direction:
_{}.

a) Find the force on the dipole using equation (6.3) of Griffiths.

b) Do the same for a dipole pointing in the

A long circular cylinder of radius *R* carries a magnetization
_{},
where *k* is a constant, *r* is the distance from the axis, and
_{}
is the azimuthal unit vector. Find the magnetic field due to
_{}
for points inside and outside the cylinder.

A short circular cylinder of radius *R* and length *L* carries a
"frozen-in" uniform magnetization
_{}
parallel to its axis. Find the bound current, and sketch the magnetic field of
the cylinder. (Make two sketches: one for *L* >> *R*, and one
for *L* << *R*.)

Of the following materials, which would you expect to be paramagnetic and
which diamagnetic? Aluminum, copper, copper chloride (CuCl_{2}),
carbon, lead, nitrogen (N_{2}), salt (NaCl), sodium,
water.