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FORCE FIELDSIB PHYSICS | UNIT 9 | FORCE FIELDS
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Static ElectricityIB PHYSICS | UNIT 9 | FORCE FIELDS
9.1
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PhET Simulation
What happens when you rub the balloon
on the sweater?
*Click Here*
Electrons transfer
from the sweater
to the balloon
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Charge on an Atom
The protons and neutrons are buried deep in the nucleus and cannot easily be
touched
electrons orbiting the nucleus are easily lost or gained
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How do objects become charged?
Friction Contact Induction
What happens when you rub John Travoltage’s
foot on the rug?
*Click Here*
The foot gains electrons
from rubbing on the
carpet and the
electrons spread out
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How do objects become charged?
Friction Contact Induction
+-
+
-
- -
- -
+-
++
-
-
Before After
+
+
+
++
Draw in the ElectronsWhat is the charge of each object?
-
-
--
- -
--
-
charge = 0 charge = -3
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+
How do objects become charged?
Friction Contact Induction
- - - - -
+
++ +
+-
+
++
+ +
+
+
+
Draw in the Electrons
Why is their hair standing up?
-
--
--
-
--
Each hair is positively
charged
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How do objects become charged?
Friction Contact Induction
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Use your knowledge responsibly
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Review of Charges
Opposite Charges Attract
Like Charges Repel
-+
- -
+
- +
+
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Which one has more force? (circle)
+
+
r
2r
Which charged pair has larger electrostatic forces acting?
+
+
smaller distance = greater force
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Which one has more force? (circle)
Which charged pair has larger electrostatic forces acting?
+r
+r
+
+
2 µC
1 µC 1 µC
1 µC
greater charge = greater force
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Coulomb’s Law
The force of attraction or repulsion between two point charges is directly proportional to the product of the two charges and inversely proportional to the square of the distance between them.
F
rF
q1
q1 q2
q2
- +
- -
F
F
Electrostatic Force 𝐹 N
Object 1 Charge 𝑞1 C
Object 2 Charge 𝑞2 C
Separation Distance 𝑟 m
𝐹 = 𝑘𝑞1𝑞2𝑟2
Symbol Unit
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Coulomb’s Constant
Use unit analysis to prove the units of k:
𝑘 = 8.99 × 109 𝑁𝑚2 𝐶−2
𝐹 = 𝑘𝑞1𝑞2𝑟2
𝑘 =𝐹𝑟2
𝑞1𝑞2=𝑁𝑚2
𝐶𝐶= 𝑁𝑚2𝐶−2
Solve for k Plug in units Simplify
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IB Physics Data Booklet
*Coulomb’s Law
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Conceptual Math
+
+
4 N
r
2r
What is the repulsion force on the positive charge below?
+
+1 N 𝐹 = 𝑘
𝑞1𝑞2(2𝑟)2
𝐹 = 𝑘𝑞1𝑞24𝑟2
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Conceptual Math
+2 Nr
What is the repulsion force on the positive charge below?
+r
+
+
2 µC
1 µC 1 µC
1 µC
4 N 𝐹 = 𝑘2𝑞1𝑞2𝑟2
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Conceptual Math
+1
+2
d
2d
Which pair has the greater electrostatic force?
+1
+2
Same!
𝐹 = 𝑘2𝑞12𝑞2(2𝑟)2
= 𝑘4𝑞1𝑞24𝑟2
= 𝑘𝑞1𝑞2𝑟2
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Electrostatic and Gravitational ForceIB PHYSICS | UNIT 9 | FORCE FIELDS
9.2
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Review of Charges
Opposite Charges Attract
Like Charges Repel
-+
- -
+
- +
+
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Coulomb’s Law
The force of attraction or repulsion between two point charges is directly proportional to the product of the two charges and inversely proportional to the square of the distance between them.
F
rF
q1
q1 q2
q2
- +
- -
F
F
Electrostatic Force 𝐹 N
Object 1 Charge 𝑞1 C
Object 2 Charge 𝑞2 C
Separation Distance 𝑟 m
𝐹 = 𝑘𝑞1𝑞2𝑟2
Symbol Unit
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IB Physics Data Booklet
*Coulomb’s Law
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Sign is important!
𝐹 = 𝑘𝑞1𝑞2𝑟2
+ F → Repel (+)(+) or (-)(-)
- F → Attract (+)(-) or (-)(+)
𝑘 = 8.99 × 109 𝑁𝑚2 𝐶−2
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Quantifying Charge
The total charge in Coulombs can be related to the number of electrons
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Quantifying Charge
The coulomb was selected to use with electric currents which makes it a very large unit for
static electricity. Get your metric prefixes ready
BA
SE U
NIT
Mill
i-(1
0-3
)m
-
Mic
ro-
(10
-6)
µ- Nan
o-
(10
-9)
n- Pic
o-
(10
-12)
p-
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Try This
Determine the electrical force of attraction between two balloons with separate charges of +3.5 x 10-8 C and -2.9 x 10-8 C when separated a distance of 0.65 m.
𝐹 = 𝑘𝑞1𝑞2𝑟2
= (8.99 × 109)(3.5 × 10−8)(3.5 × 10−8)
(0.65)2
𝐹 = −2.16 × 10−5 N
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Gravity
What is Gravity?
Idea #1: A downward force that stops you from flying away
Idea #2: An attraction towards larger objects
Idea #3: All mass attracts all other mass
Circle the answer that you agree with most
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Universal Law of Gravitation
The force of attraction between bodies with mass is directly proportional to the product of the two masses and inversely proportional to the square of the distance between them.
Gravitational Force 𝐹 N
Object 1 Mass 𝑀 kg
Object 2 Mass 𝑚 kg
Separation Distance 𝑟 m
𝐹 = 𝐺𝑀𝑚
𝑟2
M m
r
Symbol Unit
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Universal Law of Gravitation
G → Universal Gravitational Constant
G = 6.67 × 10-11 N m2 kg-2
𝐹 = 𝐺𝑀𝑚
𝑟2
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IB Physics Data Booklet
*Universal Law of Gravitation
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Gravity – Equal and Opposite
The force on the skydiver is the
same as the force on the earth but
the earth’s huge mass means that
there is hardly any acceleration
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Measuring the proper distance
Technically Newton’s Law of Gravitation defines how to calculate the gravitational force between two point masses
(Not a point mass)
Fortunately, Newton’s shell theorem states that:
“A spherically symmetric shell of mass M acts as if all of its mass is located at its center.”
r
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Try This
Determine the force of gravitational attraction between the earth (m = 5.98 x 1024 kg) and a 70-kg physics student if the student is in an airplane at 40000 feet above earth's surface. This would place the student a distance of 6.39 x 106 m from earth's center.
𝐹 = 𝐺𝑀𝑚
𝑟2= (6.67 × 10−11)
(5.98 × 1024)(70)
(6.39 × 106)2
𝐹 = 684 N
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Comparison
𝐹 = 𝐺𝑀𝑚
𝑟2𝐹 = 𝑘
𝑞1𝑞2𝑟2
Electrostatic Force Gravitational Force
𝑘 → 𝐶𝑜𝑢𝑙𝑜𝑚𝑏 𝐶𝑜𝑛𝑠𝑡𝑎𝑛𝑡 𝐺 → 𝐺𝑟𝑎𝑣𝑖𝑡𝑎𝑡𝑖𝑜𝑛𝑎𝑙 𝐶𝑜𝑛𝑠𝑡𝑎𝑛𝑡
𝑞1, 𝑞2→ Charges [C] 𝑀,𝑚 → Masses [kg]
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Permittivity
Coulomb’s Constant is sometimes expanded to this form:
𝑘 =1
4𝜋𝜀0
𝜀0 = 8.85 × 10-12 C2 N-1 m-2
𝜀0→ Permittivity of Free Space (vacuum)
*Solving for k will get Coulomb’s Constant for a vacuum
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IB Physics Data Booklet
*Solving for k
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Permittivity
Permittivity changes relative to the substance
Relative Permittivities
Free Space (a vacuum) 1
Dry Air 1.0005
Paper 4
Concrete 4
Rubber 6
𝜀𝑟 =𝜀
𝜀0
Relative Permittivity
IB might ask you about this: the higher the relative permittivity, the harder it is for electrostatic forces to travel over a distance…
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Force FieldsIB PHYSICS | UNIT 9 | FORCE FIELDS
9.3
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Warm Up
What is the force of gravity between the earth and the moon?
m = 6 × 1024 kgm = 7.4 × 1022 kg
r = 3.8 × 108 m
𝐹 = 𝐺𝑀𝑚
𝑟2
𝐹 = (6.67 × 10−11)(6 × 1024)(7.4 × 1022)
(3.8 × 108)2
𝐹 = 2.05 × 1020 N
G = 6.67 × 10-11 N m2 kg-2
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Conversion Check
7 μC → C
7 × 10-6 C
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Warm Up
A small cork with an excess charge of +7.0 µC is placed 14 cm from another cork, which carries a charge of −3.2 µC. What is
the magnitude of the electric force between the corks?
𝐹 = 𝑘𝑞1𝑞2𝑟2 k = 8.99 × 109 N m2 C-2
𝐹 = 𝑘𝑞1𝑞2𝑟2
= (8.99 × 109)(7 × 10−6)(−3.2 × 10−6)
(0.14)2
𝐹 = −10.3 N
attract
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Force Fields
Vector field that describes the force that would act on a particle at various positions
ElectricField
Gravitational Field
Sym
bo
l
𝐸 𝑔U
nit N
C= N C−1
N
kg= N kg−1
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Electric Fields
Electric Fields point in the direction that a ___________ charge would travel
+ -
positive
+
+
+
+
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Try This
+ -
Label these charges as positive (+) or negative (-)
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+
Try This
+
Predict what the field lines will look like:
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Gravity as a field
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Gravity as a field
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Gravity as a field
• The gravitational field distorts the space around the mass that is causing it so that any other mass placed at any position in the field will “know” how to respond immediately.
• Bigger masses “curve” the rubber sheet more than smaller masses.
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Gravity as a field
How do we visually represent the strength of the field?
Vector Density
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IB Physics Data Booklet
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Remember g?
g = 9.81 m s-2
g → Gravitational Field Strength
g representing acceleration is not the whole story…
𝑔 =N
kg=kg × m s−1
kg= m s−1
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Wait, does that mean g changes?
Earth Radius= 6,370 km
Orbiting Altitude = 400 km
𝑔 = 𝐺𝑀
𝑟2
400 𝑘𝑚 + 6370 𝑘𝑚 = 6770 𝑘𝑚
𝐹 = 𝐺𝑀
𝑟2= (6.67 × 10−11)
(6 × 1024)
(6,770,000)2
𝐹 = 8.73 N kg−1
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Using g
g = 8 N kg-1
g = 5 N kg-1
= 2,000,000 kg
What is the force of gravity for each position?
= 75 kg
𝐹 = (75 𝑘𝑔)(5 𝑁 𝑘𝑔−1)
𝐹 = 𝟑𝟕𝟓 𝑵
𝐹 = (2,000,000 𝑘𝑔)(5 𝑁 𝑘𝑔−1)
𝐹 = 𝟏𝟎, 𝟎𝟎𝟎, 𝟎𝟎𝟎 𝑵
𝐹 = (75 𝑘𝑔)(8 𝑁 𝑘𝑔−1)
𝐹 = 𝟔𝟎𝟎 𝑵
𝐹 = (2,000,000 𝑘𝑔)(8 𝑁 𝑘𝑔−1)
𝐹 = 𝟏𝟔, 𝟎𝟎𝟎, 𝟎𝟎𝟎 𝑵
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Try This
What is the electric field strength if a particle with a charge of +6.3 μC experiences a force of 0.0025 N?
𝐸 =𝐹
𝑞=
0.0025 N
6.3 × 10−6 C
𝐸 = 397 N C−1
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Think about this…
Two isolated point charges, –7 μC and +2 μC, are at a fixed distance apart. At which point is it possible for the electric field strength to be zero?
A B C D
-7 μC +2 μC
Forces cancel out
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Try this
What is the gravitational field strength halfway between the centers of the earth and the moon?
m = 6 × 1024 kgm = 7.3 × 1022 kg
r = 3.8 × 108 m
𝐹 = 𝐺𝑀
𝑟2G = 6.67 × 10-11 𝑁×𝑚2
𝑘𝑔2
/ 2 = 1.9 × 108 m
𝐹 = 6.67 × 10−116 × 1024
1.9 × 108 2= 𝟎. 𝟎𝟏𝟏 𝐍 𝐤𝐠−𝟏 𝐹 = 6.67 × 10−11
7.3 × 1022
1.9 × 108 2= 𝟎. 𝟎𝟎𝟎𝟏𝟑 𝐍 𝐤𝐠−𝟏
𝐹 = 0.011 − 0.00013 =
𝐹 = 0.0109 N kg−1
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Try this
Where would an object experience a gravitational field of 0 N kg-1
m = 6 × 1024 kg
r = 3.8 × 108 m
𝑔 = 𝐺𝑀
𝑟2G = 6.67 × 10-11 𝑁×𝑚2
𝑘𝑔2
re rm
m = 7.3 × 1022 kg
rm = 3.8 × 108 - re
𝐺𝑀𝑒
𝑟𝑒2= 𝐺
𝑀𝑚
𝑟𝑚2
𝑀𝑒
𝑟𝑒=
𝑀𝑚
𝑟𝑚
cancel out G
and
square root everything
𝐺𝑀𝑒
𝑟𝑒2= 𝐺
𝑀𝑚
𝑟𝑚2
6 × 1024
𝑟𝑒=
7.3 × 1022
(7.3 × 1022 − 𝑟𝑒)
9.31 × 1020 − 2.45 × 1012 𝑟𝑒 = 2.70 × 1011 𝑟𝑒
9.31 × 1020 = 2.72 × 1012 𝑟𝑒
𝑟𝑒 = 3.42 × 108 m
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Magnetism & Right Hand RuleIB PHYSICS | UNIT 9 | FORCE FIELDS
9.4
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Magnets
Magnetic materials have the ability to attract or repel other types of magnetic materials
But not all materials are magnetic
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Rules of Interaction
N S N S
N S S N
S N N S
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Cutting Magnets in Half
Poles cannot be isolated – a magnet cannot be broken to get a separate north and south pole. Instead, it creates two magnets, each with a north and south pole
N SNS
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Magnetic Domains
In order for a material with domains to become magnetic, the domains have to be aligned by an external magnetic field.
If enough of a materials domains become aligned, the material forms a magnetic dipole and becomes a permanent magnet
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Magnetic Fields
Magnetic field lines point from _________ to _________
N S
A compass would align with these field lines
North South
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B-Field
B→Magnetic Field Strength
Units
Tesla [T]
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Magnetic Fields
A horseshoe magnet is just a bent bar magnet. The rules for magnetic fields still apply.
N S
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The Earth is a Magnet
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Right Hand Rule #1
If you make a “thumbs up” sign and point your thumb down a wire in the direction of the current, your other four fingers will point in the direction of the magnetic field.
Thumb points in direction of the currentFingers point in direction of the field lines
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Drawing in 3D
It can be hard to translate a 3rd dimension into a 2-dimensional diagram so there some conventions to help us out
How do you represent a direction that’s perpendicular to the paper?
Into the paper Out of the paper
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Drawing in 3D
I
Where is Magnetic Flux Density the highest?
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Right Hand Rule #1
Draw in the magnetic field lines around these current carrying wires
I
I
I I
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Looped Wire
I
strong
B-field
weak
B-field
A wire in a loop has as stronger magnetic field inside the loop than outside…
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Creating an electromagnet
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Right Hand Rule #2
If you make curl your fingers in the direction of the current around a metal core, you will make a “thumbs up” sign where your thumb is pointing toward the north pole of the electromagnet.
II
Thumb points in toward the North Pole of the magnet
Fingers point in direction of the current N S
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Right Hand Rule #2
Label the north and south poles of these electromagnets
N
S N
S
SN
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Magnetic Field
N S
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Electromagnet Applications
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Draw in the Field Lines
N S
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Build and Study Electromagnets
Explore what factors can be changed to increase the strength of an electromagnet
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Electromagnetic ForceIB PHYSICS | UNIT 9 | FORCE FIELDS
9.5
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Remember the Right Hand Rule?
1 2Thumb points in direction of the current
Fingers point in direction of the field lines
Thumb points in toward the North Pole of the magnet
Fingers point in direction of the current
N S
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Right Hand Rule #3
Thumb points in direction of the current
Fingers point in direction of the field lines
Palm points in direction of the force
How do you represent a direction that’s perpendicular to the paper?
Into the paper Out of the paper
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S
Right Hand Rule #3
A current-carrying wire is placed in a magnetic field and the magnetic field exerts a force on the wire
N S NF
F
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Right Hand Rule
When electric current is passed through a magnetic field, you get ____________
S N
motion
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Motors vs Generators
Electric Motors convert
Electricity Motion
Electric Generators convert
Motion Electricity
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Examples
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Speakers
S N S N
F
F
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Definition of the Ampere
**One ampere is defined as the current that would cause a force of 2 × 10-7 N per meter between two long parallel conductors separated by 1 m in a vacuum
Consider two parallel wires, with current in the same direction. Do they attract or repel??
F
F
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Fields
Gravitational Field
Electric Field
Magnetic Field
𝑔 =𝐹
𝑚=
N
kg
𝐸 =𝐹
𝑞=
N
C
𝐵 =𝐹
𝐼=
N
A= T
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Magnetic Flux
The magnetic field strength is sometimes referred to as magnetic flux and depends on how perpendicular the current is in relation to the field direction
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Magnetic field Strength
Current, I
Length of wire in field, L
θ
θAngle between field and current
The force on the wire is proportional to the charge moving perpendicular to the field. Because of these the perpendicular component must be used in the calculation
𝐵 =𝐹
𝐼𝐿𝑠𝑖𝑛𝜃
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Fields
𝐵 =𝐹
𝐼𝐿 𝑠𝑖𝑛𝜃𝐹 = 𝐵𝐼𝐿 𝑠𝑖𝑛𝜃
FMagnetic forceNewtons [N]
BMagnetic field strengthTesla [T]
ICurrentAmperes [A]
LLength of conductor in uniform magnetic field
θAngle between magnetic field and current
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IB Physics Data Booklet
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Try This…
A current of 3.8 A in a long wire experiences a force of 5.7 × 10-3 N when it flows through a magnetic field of strength 25 mT. If the length of wire in the field is 10 cm, what is the angle between the field and current?
𝐹 = 𝐵𝐼𝐿 𝑠𝑖𝑛𝜃
𝜃 = 𝑠𝑖𝑛−1𝐹
𝐵𝐼𝐿= 𝑠𝑖𝑛−1
(5.7 × 10−3)
(25 × 10−3)(3.8)(0.1)
𝜃 = 36.87°𝐹 = 5.7 × 10−3 N
𝐵 = 25 mT = 25 × 10−3 T
𝐼 = 3.8 A
𝐿 = 10 cm = 0.1 m
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Force on a Charged Particle
When there is an magnetic force on a current carrying wire, the force is really on the moving charges inside of the conductor.
Single charged particles can also experience a magnetic force when moving through a magnetic field…
𝐹 = 𝐵𝐼𝐿 𝑠𝑖𝑛𝜃 + 𝑣 =𝐿
𝑡
𝐼 =𝑞
𝑡
𝐿 = 𝑣𝑡𝐹 = 𝐵 𝑞
𝑡𝑣𝑡 𝑠𝑖𝑛𝜃
𝐹 = 𝐵𝑞𝑣 𝑠𝑖𝑛𝜃
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IB Physics Data Booklet
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Try This…
What is the magnetic force acting on a proton (+1.6 × 10-19 C) moving at an angle of 32° across a magnetic field of 5.3 × 10-3 T at a speed of 3.4 × 105 m s-1?
𝐹 = 𝑞𝑣𝐵 𝑠𝑖𝑛𝜃𝐹 = 1.6 × 10−19 3.4 × 105 5.3 × 10−3 𝑠𝑖𝑛32°
𝐹 = 1.5 × 10−16 N𝑞 = 1.6 × 10−19 C
𝑣 = 3.4 × 105 m s−1
𝐵 = 5.3 × 10−3 T
𝜃 = 32°
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Particles Moving Across Fields
magnetic field out of screen magnetic field into screen
+
+
-
-
fast
slow