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Magnetism – part 2
Some of the subtleties
Magnetic field around
current-carrying wire
 current through wire   magnetic field
𝐼𝛼𝐵
Strength of magnetic field
If you enclose a wire with a series of short
imaginary lines of length l along which you
measure the strength of the magnetic field,
the sum of the strength of the magnetic field
is 𝑙𝑜𝑜𝑝 𝐵∆𝑙 α 𝐼
𝐵∆𝑙 = 𝜇0 𝐼
𝑙𝑜𝑜𝑝
Proportionality constant, 0,
• Pronounced “mu naught”
• Called permeability of free space
𝑚
• Value of 4 𝑥 10−7 𝑇
𝐴
Ampere’s Law
𝐵∆𝑙 = 𝜇0 𝐼
𝑙𝑜𝑜𝑝
Where 𝑙𝑜𝑜𝑝 ∆𝑙 averages
out to be the perimeter
of a circle, = 2π𝑟
B(2π𝑟) = 𝜇0 𝐼
𝜇0 𝐼
B=
2𝜋 𝑟
Implications
𝜇0 𝐼
B=
2𝜋 𝑟
 current through wire   magnetic field
 distance from wire   magnetic field
One of four fundamental laws
of electricity and magnetism!*
*
Usually written as
𝐵 𝑑𝑙 = 𝜇𝑜 𝐼𝑒𝑛𝑐𝑙𝑜𝑠𝑒𝑑
Example
An electric wire carries a
current of 25 A vertically
Try
first.𝐴
𝐼 =it 25
Try it first.
upward. What is the magnetic
𝜇0 𝐼
B=
2𝜋 𝑟
field due to this current 0.10 m
Try it first.
due north of the wire? In what
direction does it point?
𝑑 = 0.10 𝑚
4𝜋 x 10−7 25 𝐴
B=
2𝜋
0.10 𝑚
Try it first.
B = 5.0 x
10−5
𝑇
Try it first.
Direction? right hand thumb up in
direction of current, fingers curl.
North of wire, fingers point west.
Note: most electric
wiring consists of two
wires in each cable.
Since two wires carry
current in opposite
directions, their
magnetic fields mostly
cancel.
Applications of magnetism
• Electromagnets
• Solenoids
• Electrical relays
• Doorbells
• Ground fault circuit interrupter
• Loudspeakers
• Gauges
• Mass spectrometers
• Seismographs
• Microphones
• Credit card readers
Electromagnets
DIY: link




number of coils, N   B
current, I   B
Length of wire, l   B
permeability of core,   B
Permeability of most materials ~ 0
Permeability of iron ~ 200,000 x 0
Scrap yard: link
𝜇𝑁𝐼
B=
𝑙
Loudspeakers
Varying electrical current runs
through coil of wires suspended in
magnetic field.
• Magnetic field induced by current
causes coil to be attracted to or
repulsed by magnet.
• Pushes and pull on coil cause
attached diaphragm to push air in
exactly same pattern as electrical
input, i.e., reproduce sounds used
to create electrical current.
Longer explanation here.
•
Analog gauges
Pivot axle is attached to
spring (provides resistance),
pointer (allows for
measurement), and coil of
wires surrounding a core
between poles of magnet.
For more information on
galvanometers: link
Mass spectrometer
Mass spectrometers allow physicists,
chemists, geologists, medical doctors,
and others to measure
the
mass of atoms by applying
knowledge of electricity and
magnetism.
1.The sample is
forced to release
ions, typically by
heating it up.
2. Some of the ions
pass through slit 1,
S1.
3. Those ions pass
through a charged
capacitor in a
magnetic field, i.e.,
they experience an
electric AND
magnetic field.
4. If the electric force
on the ion is
balanced by the
magnetic force
experienced by the
ion, the ions pass
through slit 2, S2.
5. Those ions pass
into a region with a
strong magnetic
field but no electric
field.
6. The radius of the
deflection of the
ions is a function of
their mass.
7. The detector can
be either a
photographic plate
or an electrically
sensitive screen
Background physics
Recall the force experienced by a charged
particle in an electric field is given by
𝐹 = 𝑞𝐸
where q = charge (C)
E = strength of electric field
(in V/m or, equivalently,
N/C)
Background physics
The force experienced by a moving charged particle in a magnetic field
is given by the following relationship:
𝐹 = 𝑞𝑣𝐵sinθ
where q = charge
v = velocity
B = strength of magnetic field
 = angle between direction of particle’s motion and
magnetic field (when the particle is moving
perpendicular to the field, sin  = 1)
Getting through slit 2
The only ions that will pass through slit 2 are those which experience
no net force, i.e., particles on which the magnetic and electric forces
are equal.
𝐹𝑒𝑙𝑒𝑐𝑡𝑟𝑖𝑐 = 𝐹𝑚𝑎𝑔𝑛𝑒𝑡𝑖𝑐
or
𝑞𝐸 = 𝑞𝑣𝐵
In other words, ions must be traveling at speed, 𝑣
slits 2.
=
𝐸
to get through
𝐵
Background physics
The force required to move an object
in circular motion is given by the
following equation:
𝑚𝑣2
𝐹=
𝑟
where m = mass
v = velocity
r = radius of circle
Curving in magnetic field
When the ions pass through slit 2, they are forced into circular motion
by the magnetic field.
𝐹𝑐𝑒𝑛𝑡𝑟𝑖𝑝𝑒𝑡𝑎𝑙 = 𝐹𝑚𝑎𝑔𝑛𝑒𝑡𝑖𝑐
or
𝑚𝑣 2
= 𝑞𝑣𝐵
𝑟
So
𝑞𝐵𝑟 𝑞𝐵2 𝑟
𝑚=
=
𝑣
𝐸
Example
Mass spectrometers can be used to calculate
relative age of carbon-based materials by
measuring ratio of isotope carbon-14 (which is
absorbed into living tissue at a low but steady rate
and decays in dead tissue at a predictable rate) to
carbon-12.
The mass of C-14 is 14 x 1.67 x 10-27 kg.
The mass of C-12 is 12 x 1.67 x 10-27 kg.
Example
Suppose spectrometer’s electric
field is 2.88 x104 N/C and the
magnetic field is 0.68 T. If you
send ionized C-12 and C-14
through the spectrometer, how
far apart will the singly-charged
isotopes be detected?
Assume the ions travel ½ the
perimeter of a circle before
detection.
𝑁
Identify
the unknowns
𝐸 = 2.88
𝑥 104
𝐶
𝐵 = 0.68 𝑇
𝑚𝐶14 = 14 𝑥 1.67 𝑥 10−27 𝑘𝑔
𝑚𝐶12 = 12 𝑥 1.67 𝑥 10−27 𝑘𝑔
𝑞 = 1.60 𝑥 10−19 𝐶
Consider
physical
system.½
It’sperimeter
not enough toofcalculate
Isotopestheare
traveling
circle,
the radius
so distance between source and detection
will be 2 x (rC14-rC12)
Example
Suppose spectrometer’s electric
field is 2.88 x104 N/C and the
magnetic field is 0.68 T. If you
send ionized C-12 and C-14
through the spectrometer, how
far apart will the singly-charged
isotopes be detected?
Assume the ions travel ½ the
perimeter of a circle before
detection.
𝑞𝐵2 𝑟
Try it first.
𝑚=
𝐸
Try it
first.
𝑑 = 2𝑟
Try it first.
=2
so, 𝑟 =
𝑚𝐸
𝑞𝐵2
Try it
Try it first.
𝐸
first. 𝑚𝐸
= 2 2 = 2 2 (𝑚𝐶14
𝑞𝐵
𝑞𝐵
𝑁
2.88 𝑥104 𝐶
1.67 𝑥 10 −19𝐶 0.68𝑇
Try
𝑑 =it first.
2.6 𝑥10−3 𝑚
2
− 𝑚𝐶12 )
14 − 12 𝑥10−27 𝑘𝑔
Who cares?
Isotopic dating
Understand
chemical
reactions
Discover
isotopes
Infer chemical
composition
For more information on
mass spectra, search for
images of <mass
spectra> + <compound
or element of interest>