FACULTY OF SCIENCE, WINTER 2008
PHYS 126 LEC B3 : Fluids, Fields and Radiation
(Instructor: Marc de Montigny)
Walker, Physics, Chapter 22: Magnetism
- Section 22-1: The Magnetic Field
- Magnetic Field B is a vector. Unit: Tesla (T). In geomagnetism
we use also Gauss (G) [1 G = 10-4 T]
- We consider magnetic fields acting (1) on moving charges (mostly), and (2) on magnets.
- Figure 22-1 shows the force between two bar
magnets.
- A magnet contains two poles, north and south, which cannot be isolated, unlike
electric charges, as illustrated in Figure 22-2 .
- This simulation
shows the effect of a magnetic field on a compass (bar magnet).
- Magnetic field lines
can be used in much the same way as electric field lines
to represent the magnitude and direction of magnetic fields. The more closely
spaced the lines, the more intense the field. Magnetic field lines always form
closed loops, and they point away from north poles and toward south poles.
- By definition, the direction of the
magnetic field B at a given
location is the direction in which the north pole of a compass points
(i.e. towards the south pole) when placed at that location.
- Figure 22-6 shows the magnetic field of the
Earth:
- The north geographical pole is actually near the south pole of the
Earth's magnetic field.
- The magnetic poles are tilted away from the rotation axis by about
11.5o.
- This angle changes. It has even reversed many times over the ages
(last time, about 780,000 years ago).
- Section 22-2: The Magnetic Force on Moving Charges
- If a charge q is moving with velocity v in a magnetic
field B, then the magnetic force FB is given
by the cross product: FB =
q v × B. The cross product is reviewed in
Appendix 9 of Walker's text. We encountered it in PHYS 124, in
Chapter 11 on rotation dynamics because the torque is defined
also as a cross-product.
- P. 735, Eq. 22-2, Magnitude of the magnetic force: F = |q| vB sinθ.
The term sinθ means that if v and B are parallel or
anti-parallel to one another, then no force is produced; a perpendicular
component (v w/r B, or B w/r v) is needed.
- The direction of F is obtained from v and B by the
right-hand rule (Figure 22-8).
- Simulation
for the cross product.
- Eq. 22-2 can be understood as the definition of the magnetic field B,
so that, as in Eq. 22-3, B = F/(|q|v sinθ).
- Unit of B: 1 tesla (T) = 1 N/(A•m)
- P. 738: F = qv×B
- P. 762, Problem 8
- P. 765, Problem 62
- P. 740, Conceptual CheckPoint 22-3
- P. 763, Problem 16
- Section 22-3: The Motion of Charged Particles in a Magnetic Field
- Section 22-4: The Magnetic Force Exerted on a Current-Carrying Wire
- P. 744, Eq. 22-4, Magnetic force on a current-carrying wire: F = ILB sinθ
- Vector form: F = IL×B
- P. 763, Problem 24
- P. 763, Problem 30
- Section 22-5: Loops of Current and Magnetic Torque
- P. 747, Eq. 22-6, Torque exerted on a general loop of area A and N turns:
τ = NIAB sinθ.
- P. 746, Figure 22-16 shows the magnetic
forces on a current loop.
- P. 747, Figure 22-17 shows the magnetic
torque on a current loop.
- Remark: Eq. 22-6 can be expressed as the vector product
τ = μ×B, where μ is the 'magnetic moment'
of the loop. Its magnitude μ = NIA, and its direction is given by the right-hand
rule: the thumb points in the direction μ when the fingers are curled
in the direction of the current I, as shown in
this figure.
- P. 764, Problem 37
- Section 22-6: Electric Currents, Magnetic Fields [Ampère's Law is OMITTED]
- P. 750, Eq. 22-9, Magnetic field for a long, straight wire: B = μ0I/(2πr)
- P. 750, Eq. 22-8: Permeability of free space μ0 = 4π×10-7
T•m/A
- P. 749, Figure 22-19 shows the direction of the magnetic
field of a current-carrying wire. This is determined by the right-hand rule, as shown
in Figure 22-20.
- P. 752, Eq. 22-10, Force between current-carrying wires:
F = μ0I1I2L/(2πd).
Figure 22-23 shows the field produced by I1, and
the force F thereby produced on I2.
- P. 764, Problem 43
- P. 766, Problem 70
- Section 22-7: Current Loops and Solenoids
- P. 753, Eq. 22-11, Magnetic field produced by a current loop:
B = Nμ0I/(2R). The right-hand rule gives the
direction of the field, as in Figure 22-25.
- P. 754, Eq. 22-12, Magnetic field produced by a solenoid:
B = μ0(N/L)I = μ0nI. Once again, the right-hand rule gives the
direction of the field, as in Figure 22-27:
curl your fingers along the current I and the thumb points in the direction of
B inside the solenoid.
- Section 22-8: Magnetism in Matter
- P. 755, Ferromagnetism: A ferromagnetic material produces a magnetic field even
in the absence of an external magnetic field. Permanent magnets are constructed
of ferromagnetic materials.
- P. 756, Paramagnetism: A paramagnetism material has no magnetic field unless an
external magnetic field is applied to it. In this case, it develops a magnetization
in the direction of the external field.
- P. 756, Diamagnetism: Diamagnetism is the effect of the production by a material
of a magnetic field in the opposite direction to an external magnetic field that is
applied to it. All material show at least a small diamagnetic effect.
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