Transcript 20.6 Force between Two Parallel Wires

20.6 Force between Two Parallel Wires
The magnetic field produced
at the position of wire 2 due to
the current in wire 1 is:
The force this field exerts on
a length l2 of wire 2 is:
(20-7)
20.6 Force between Two Parallel Wires
Parallel currents attract; antiparallel currents
repel.
Example 20-10
The two wires of a 2.0 m long appliance cord are 3.0 mm apart and carry a
current of 8.0 A dc. Calculate the force one wire exerts on the other.
F=
0 I1I 2
l2
2 d
(2.0x10 -7 Tm/A)(8.0 A) 2 (2.0 m)
F=
(3.0x10 -3 m)
F = 8.5x10 -3 N
The currents are in opposite directions (one toward the appliance, the other
away from it),so the force would be repulsive and tend to spread the wires
apart.
Example 20-11
A horizontal wire carries a current I1=80 A dc. A second parallel wire 20 cm
below it must carry how much current I2 so that it doesn’t fall due to gravity?
The lower wire has a mass of 0.12 g per meter of length.
F = mg = (0.12x10 -3 kg/m)(9.8 m/s 2 ) = 1.18x10 -3 N/m
0 I1I 2
2d F
F=
l  I2 =
2 d
0I1 l
2 (0.20 m)(1.18x10 -3 N/m)
I2 =
= 15 A
-7
(4 x10 Tm/A)(80 A)
20.7 Solenoids and Electromagnets
A solenoid is a long coil of wire. If it is tightly
wrapped, the magnetic field in its interior is
almost uniform:
(20-8)
20.7 Solenoids and Electromagnets
If a piece of iron is inserted in the solenoid, the
magnetic field greatly increases. Such
electromagnets have many practical
applications.
20.8 Ampère’s Law
Ampère’s law relates the
magnetic field around a
closed loop to the total
current flowing through
the loop.
(20-9)
20.8 Ampère’s Law
Ampère’s law can be used to calculate the
magnetic field in situations with a high degree
of symmetry.
20.9 Torque on a Current Loop; Magnetic
Moment
The forces on opposite sides of a current loop
will be equal and opposite (if the field is
uniform and the loop is symmetric), but there
may be a torque.
The magnitude of the torque is given by:
(20-10)
The quantity NIA is called the magnetic
dipole moment, M:
(20-11)
Example 20-12
A circular coil of wire has a diameter of 20.0 cm ad contains 10 loops. The
current in each loop is 3.00 A, and the coil is placed in a 2.00 T external
magnetic field. Determine the maximum and minimum torque exerted on the
coil by the field.
A = r 2 =  (0.100 m) 2 = 3.14x10 -2 m
Max torque means sin  = 1
 = NIABsin  = (10)(3.00 A)(3.14x10 -2 m)(2.00 T)(1) = 1.88 Nm
Min torque means sin  = 0
 = NIABsin  = 0

20.10 Applications: Galvanometers,
Motors, Loudspeakers
A galvanometer
takes advantage of
the torque on a
current loop to
measure current.
20.10 Applications: Galvanometers,
Motors, Loudspeakers
An electric motor
also takes
advantage of the
torque on a current
loop, to change
electrical energy to
mechanical energy.
20.10 Applications: Galvanometers,
Motors, Loudspeakers
Loudspeakers use the
principle that a magnet
exerts a force on a
current-carrying wire to
convert electrical
signals into mechanical
vibrations, producing
sound.
20.11 Mass Spectrometer
A mass spectrometer measures the masses of
atoms. If a charged particle is moving through
perpendicular electric and magnetic fields,
there is a particular speed at which it will not
be deflected:
20.11 Mass Spectrometer
All the atoms
reaching the second
magnetic field will
have the same
speed; their radius of
curvature will depend
on their mass.
Example 20-13
Carbon atoms of atomic mass 12.0 u are found to be mixed with another,
unknown, element. In a mass spectrometer with fixed B’, the carbon
traverses a path of radius 22.4 cm and the unknown’s path has a 26.2 cm
radius. What is the unknown element? Assume they have the same
charge.
mx qBB' rx /E 26.2 cm
=
=
= 1.17
mc qBB' rc /E 22.4 cm
mx = 1.17x12.0 u = 14.0 u, which corresponds
to nitrogen

20.12 Ferromagnetism: Domains and
Hysteresis
Ferromagnetic materials are those that
can become strongly magnetized, such as
iron and nickel.
These materials are made up of tiny
regions called domains; the magnetic field
in each domain is in a single direction.
20.12 Ferromagnetism: Domains and
Hysteresis
When the material is
unmagnetized, the
domains are randomly
oriented. They can be
partially or fully aligned by
placing the material in an
external magnetic field.
20.12 Ferromagnetism: Domains and
Hysteresis
A magnet, if undisturbed, will tend to retain its
magnetism. It can be demagnetized by shock or
heat.
The relationship between the external magnetic
field and the internal field in a ferromagnet is
not simple, as the magnetization can vary.
20.12 Ferromagnetism: Domains and
Hysteresis
Starting with unmagnetized
material and no magnetic
field, the magnetic field can
be increased, decreased,
reversed, and the cycle
repeated. The resulting plot
of the total magnetic field
within the ferromagnet is
called a hysteresis curve.
Summary of Chapter 20
• Magnets have north and south poles
• Like poles repel, unlike attract
• Unit of magnetic field: tesla
• Electric currents produce magnetic fields
• A magnetic field exerts a force on an electric
current:
Summary of Chapter 20
• A magnetic field exerts a force on a moving
charge:
• Magnitude of the field of a long, straight
current-carrying wire:
• Parallel currents attract; antiparallel
currents repel
Summary of Chapter 20
• Magnetic field inside a solenoid:
• Ampère’s law:
• Torque on a current loop:
Homework - Ch. 20
• Questions #’s 2, 3, 4, 5, 6, 14, 15
• Problems #’s 3, 7, 11, 15, 21, 29, 37, 49,
51, 53, 55, 61, 65