Transcript Faraday`s Law

Electromagnetism
Faraday & Maxwell
Faraday
Michael Faraday (1791 – 1867)
was an English scientist. He
was a genius at experimental
design and conceptualization
(and an incompetent mathematician).
Observations
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Holding a magnet in front of a coil of wires
does not induce a current.
Pushing the north pole of a magnet through
the coil induces a current in one direction.
Pulling the north pole of a magnet back out
of the coil induces a current in the other
direction.
The bigger the area of the coil, the larger the
current.
Twisting a magnet in front of a coil of wires
causes a current only while the magnet is
moving.
Rutgers: example
Induction
A changing magnetic field
around a coil of wires
induces a potential
difference, .
Investigate this simulation.
Induction
A changing magnetic environment
around a coil of wires induces a
potential difference, .
 Strength of magnet   voltage
 Area of coil   voltage
 Number of coils   voltage
 Rate of change of magnetic field
  voltage
𝜀𝛼𝐵
𝜀𝛼𝐴
𝜀𝛼𝑁
1
𝜀𝛼
∆𝑡
Flux
In physics, when we talk about
“flux”, we refer to the number
of things passing through or
hitting a certain area.
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•
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Number of tennis balls
landing in a particular area on
the tennis court
Number of photons hitting
your retina
Number of magnetic field
lines passing through a
particular area.
Flux
For purposes of electromagnetism,
magnetic flux refers to the strength of
magnetic field times the area:
1 tesla  1 square meter = 1 weber
1 W = 1 T  1 m2
We use the Greek letter phi
(pronounced ‘fee’ or ‘fie’) subscript B to
denote magnetic flux, B
Wilhelm Weber, German,
1804 – 1891: investigated
electricity and magnetism,
co-invented telegraph.
More here
Changing flux:
1) With magnets of
different strength
B results in denser
field lines and   B
Changing flux:
2) With different sizes
of coils
A results in more
field lines and   B
Changing flux:
3) At different angles
 results in more field
lines and   B
At different angles (cont’d)
B  B
where B = component of
magnetic field
perpendicular to
coil
= B (cos )
B  B (cos )
Changing flux: summary
𝐵 = 𝐵 𝐴 cos
Where B = strength of magnetic field
A = area of coil
cos  = angle between normal
(face of coil) and direction
of magnetic field
How do we change induced current?
A current is induced when
there is a change in the
magnetic flux through the
loop’s area.
B   
t   
N   
This relationship is called Faraday’s Law
(but was articulated by James Maxwell)
=𝑁
∆𝐵
∆𝑡
=
∆(𝐵 𝑐𝑜𝑠𝜃 𝐴)
𝑁
∆𝑡
Example
A square loop of wire with side length, l = 5.0 cm
is in a uniform magnetic field, B = 0.16 T. What is
the magnitude of the magnetic flux in the loop
when B is perpendicular to the face of the loop?
−2 𝑚 2 (cos 0°)
Try it first
𝐵 =Try𝐵it first
𝐴 cos = 0.16 𝑇 5𝑥10
𝐵 = 4𝑥10−4 𝑇Try𝑚it 2first= 4𝑥10−4 W
Example
A square loop of wire with side length, l = 5.0 cm is
in a uniform magnetic field, B = 0.16 T. What is the
magnitude of the magnetic flux in the loop when B is
at an angle of 30 to the face of the loop?
Try it −2
first𝑚 2 (cos 30°)
𝐵 =Try𝐵it first
𝐴 cos = 0.16 𝑇 5𝑥10
𝐵 = 3.5𝑥10−4 W
Try it first
Example
Suppose you rotate a square
coil of wires with side length
5.0 cm in a magnetic field of
strength 0.16 T. If it takes the
coil 0.14 s to go from being
perpendicular to the field to
30, how much current flows?
Assume a resistor of 0.012 .
𝑉
𝑉 = Try
𝐼𝑅it𝑠𝑜
first𝐼 =
𝑅
∆(𝐵 𝑐𝑜𝑠𝜃 𝐴)
Where 𝑉 = 𝜀 Try
= it first
∆𝑡
So, 𝐼 =
𝐵∆ 𝑐𝑜𝑠𝜃 𝐴
Try it first
𝑅 ∆𝑡
−2 𝑚
0.16 𝑇 𝑐𝑜𝑠0°
−
cos
30
°
5
𝑥
10
Try it first
𝐼=
(0.012 ) (0.14 𝑠)
𝐼 = 0.030 𝐴
Try it first
2
“Motional”

Suppose you had a conducting bar
connecting two parallel wires length L
apart that ran perpendicular to an
external magnetic field. If you were to
slide the bar some distance x, you would
increase the area and induce a current.
𝐵 = 0, so cos  = 1
𝑁 = 1
𝐴 = 𝐿𝑥
𝑚𝑜𝑡𝑖𝑜𝑛𝑎𝑙
𝐵(𝑐𝑜𝑠𝜃)𝐴
∆𝑥
=𝑁
= 𝐵𝐿
= 𝐵𝐿𝑣
∆𝑡
∆𝑡
Example
Since blood contains ions, we can infer
speed of blood flow if we place a test
subject in a known magnetic field and
measure the resulting current.
Suppose a blood vessel is 2.0 mm in
diameter, the magnetic field is 0.080 T,
and the measured emf is 0.10 mV.
What is the flow velocity of blood?
Example
Suppose a blood vessel is 2.0 mm in diameter, the magnetic
field is 0.080 T, and the measured emf is 0.10 mV. What is
the flow velocity of blood?
it first so 𝑣 =
 =Try𝐵𝐿𝑣
𝑣=
𝑚
Try
it first
0.63
𝑠

𝐵𝐿
=
0.10 𝑥10−3 𝑉
Try it first
0.080 𝑇 2.0 𝑥10−3 𝑚
Applications
Generators
Animal navigation
Solid waste recycling
Burglar alarms
Metal detectors
Speakers
Seismometers
Ground-fault circuit interrupters
Computer memory
Inductive chargers
Etc.
Transformers
• It is more efficient to carry
electricity long distances at high
voltage.
• However, high voltage can be very
dangerous so is less useful in most
situations.
• A transformer is a device for
increasing or decreasing the
voltage of an alternating current
(ac).
Understanding transformers
Alternating current
in primary coil
results in changing
magnetic field in
iron core
Changing magnetic
field propagates
through iron core.
Changing magnetic
field induces
current in
secondary coil
Physics of transformers
𝑠𝑒𝑐𝑜𝑛𝑑𝑎𝑟𝑦 = 𝑁𝑠𝑒𝑐𝑜𝑛𝑑𝑎𝑟𝑦
∆𝐵
where
=
∆𝑡
So,
𝑠𝑒𝑐𝑜𝑛𝑑𝑎𝑟𝑦
𝜀𝑝𝑟𝑖𝑚𝑎𝑟𝑦
=
∆𝐵
∆𝑡
𝜀𝑝𝑟𝑖𝑚𝑎𝑟𝑦
𝑁𝑝𝑟𝑖𝑚𝑎𝑟𝑦
𝑁𝑠𝑒𝑐𝑜𝑛𝑑𝑎𝑟𝑦
𝑁𝑝𝑟𝑖𝑚𝑎𝑟𝑦
More…
Efficient transformers are typically more than 99% efficient, so
𝑃𝑝𝑟𝑖𝑚𝑎𝑟𝑦 = 𝑃𝑠𝑒𝑐𝑜𝑛𝑑𝑎𝑟𝑦
So,
(𝐼𝑉)𝑝𝑟𝑖𝑚𝑎𝑟𝑦 = (𝐼𝑉)𝑠𝑒𝑐𝑜𝑛𝑑𝑎𝑟𝑦
Or
𝐼𝑠 𝑉𝑝
=
𝐼𝑝 𝑉𝑠
Example
The charger for a cell phone
contains a transformer that
reduces 120-V alternating
current to 5.0 V ac. Suppose
the secondary coil contains 30
turns and the charger supplies
700 mA.
𝑉𝑠
𝑉𝑝
=
𝑁
, so
𝑁𝑝
Try𝑠it first
𝑁𝑠
30
𝑁𝑝 =
= Try it first
Try it𝑉
first
5
𝑠
120
𝑉𝑝
Try it first
= 720 𝑡𝑢𝑟𝑛𝑠
How many turns in the primary
coil?
Example
The charger for a cell phone
contains a transformer that
reduces 120-V alternating
current to 5.0 V ac. Suppose
the secondary coil contains 30
turns and the charger supplies
700 mA.
What is the current in the
primary coil?
𝐼𝑃
𝐼𝑠
𝑁𝑠
= Try it ,first
so
𝑁𝑝
𝑁𝑠
30
Try it first 𝐼 =
Try
it first 𝐴)
𝐼𝑝 =
(0.70
𝑠
𝑁𝑝
720
= 29 𝑚𝐴Try it first
Example
The charger for a cell phone
contains a transformer that
reduces 120-V alternating
current to 5.0 V ac. Suppose
the secondary coil contains 30
turns and the charger supplies
700 mA.
How much power is
transformed?
it first
𝑃 =Try𝐼𝑉
Try it first
𝑃 = 0.70
𝐴 5𝑉
= 3.5 𝑊Try it first
Typical power lines
Lenz’s Law
Changing magnetic fields lead
to induced currents:
∆𝜑𝐵 → 𝜀
Those induced currents lead
to induced magnetic fields.
𝜀→𝐵
Those induced magnetic fields
resist further change to
magnetic flux.
𝐵 →↓ ∆𝜑𝐵
If you want to induce currents,
you have to do work.
∆𝐵
 = −𝑁
∆𝑡
Electromagnetic waves
A changing electric field can induce a magnetic field.
A changing magnetic field can induce an electric field.
Therefore, it should be possible to create a self-sustaining electric and
magnetic field independent of charges or currents!
A changing electric field creates a magnetic field which then changes
in just the right way to recreate the electric field which changes to
recreate the magnetic field… etc.
These are electromagnetic waves (more about which to come).