Note again the presence of the vector cross productin this equation: the direction ofwill be perpendicular
to the plane containingmandB, in a right-hand sense.
Now suppose we put a magnetic dipole (e.g. a bar magnet or wire coil) of magnetic momentmin a
magnetic fieldB. What will happen? Ifmis parallel or anti-parallel toB(so the bar magnet is aligned with
B, or the plane of the wire coil is perpendicular toB), then the torque on the dipole will be zero, and nothing
will happen—the dipole will remain stationary. But if we displace the dipole from this position, then there
will be a non-zero torque on the dipole, in a direction that will rotate the dipole back toward the direction of
B. But once the dipole momentmis aligned withB, the dipole’s inertia will make it overshoot and rotate past
B, where it will experience a torque that will make it rotate back towardBagain, etc. The resulting motion
will be that magnetic dipole will oscillate back and forth about theBdirection, with simple harmonic motion.
The period of this oscillating motion will depend, in part, on the strength of the magnetic field; in fact, this
method was once used to measure magnetic field strength. One would measure the period of oscillation of a
well-calibrated dipole in a magnetic field, and use the resulting period to findB.
31.12 Magnetic Pressure
The magnetic field can be thought of a producing apressure, given by
PD
B^2
2 0
; (31.12)
wherePis the pressure in pascals (Pa; 1 Pa = 1 N/m^2 ). This magnetic pressure can be used to relate the
“force” rating of a permanent magnet (which is the maximum weight it is supposed to be able to lift) to the
magnetic field strengthBat the pole face. SupposeFis the magnet’s force rating, and the pole face has area
A. Then the magnetic pressure isPDF=A,so
PD
F
A
D
B^2
2 0
; (31.13)
So the force ratingFis related to the magnetic field strength at the pole faceBby
FD
AB^2
2 0
: (31.14)
Example.Suppose we have a 100-lb magnet whose pole face is 15 in4.5 in. (The 100-lb rating means
that the magnet is capable of lifting loads that weigh up to 100 pounds.) What is the magnetic field strength
Bat the pole face?
Solution.First, convert everything to SI units: the pole face is 38.1 cm11.43 cm, andFD444:8222
N. Then the areaAof the pole face isAD.0:381m/.0:1143m/D0:043548m^2. By Eq. (31.14), the
magnetic field at the pole face is given by
BD
r
2 0 F
A; (31.15)
or
BD
s
2.4 10 ^7 N=A^2 /.444:8222N/
0:043548m^2