Download lecture 27 magnetic fields

LECTURE 27
MAGNETIC FIELDS
Instructor: Kazumi Tolich
Lecture 27
2
! 
Reading chapter 22-6 and 22-7.
!  Magnetic
field due to current
!  Ampere’s law
!  Current loops and solenoid
Magnetism from moving charges
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! 
! 
A moving charge generates a magnetic field.
The magnetism inside bar magnets are due to
electrons moving within the atoms.
! 
! 
! 
The orbiting electrons act like a magnet.
If these tiny magnets line up, they act like a big magnet.
According to the dynamo theory,
Earth’s magnetic effects are due to
electrically charged material flowing
(convection of molten iron) inside
Earth.
Magnetic field due to current
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! 
! 
Electric current can create
magnetic fields.
These magnetic fields
form circles around the
current.
Direction of the magnetic field
5
! 
The direction of the magnetic field can be found by
the right hand rule.
!  Point
your thumb in the direction of the current, and
your fingers will curl in the direction of the B field.
The B field produced by a current
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a) 
b) 
There is no current, so no B field is produced.
With current, B field pointing perpendicular to the
wire is produced.
B due to current in a long straight wire
7
! 
The magnitude of magnetic field at a distance
r away from a long straight wire carrying a
current I is given by
µ0 I
B=
2π r
where µ0 = 4π × 10-7 T"m/A is the
permeability of free space.
Example: 1
8
! 
A long, straight wire
carries a current of
I = 7.2 A. How far from
this wire is the magnetic
field it produces equal
to the Earth’s magnetic
field, which is
approximately
B = 5.0 × 10-5 T?
Superposition of B
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If there are multiple sources of magnetic field, the
magnetic field at a particular location is the
superposition of magnetic field due to each source.
!  Since magnetic field is a vector quantity, you need
to add magnetic field vectorially.
! 
Clicker question: 1
10
Example: 2
11
! 
Two long parallel wires
carrying currents i1 and i2 in
opposite directions. What is
the resultant magnetic field
at point P? Assume i1 = 15 A,
i2 = 32 A, and d = 5.3 cm.
Ampere’s law
12
! 
Ampere’s law relates the
current through a surface
defined by a closed path to
the magnetic field along the
path:
∑ B ΔL = µ I
!
!  This
0 enclosed
holds provided that the
current is constant.
Amperian loop
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Ampere's law holds for any closed path.
!  The closed path used in Ampere's law is called the
amperian loop.
!  An amperian loop is an imaginary path that you
construct.
!  If any two amperian loops enclose the same current,
∑ B!ΔL is the same, regardless of their shapes.
! 
Calculating B fields using Ampere's law
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Ampere's law is true for all situations, but not
useful in finding B unless the current is highly
symmetric.
!  In choosing the amperian loop:
! 
!  The
B field is either parallel (B! ΔL = BΔL ) or
perpendicular ( B! ΔL = 0 ) to the sections of the loop.
!  If the B field is parallel to a section of the loop, the
magnitude of the B field is constant along that part
of the loop.
Ampere’s law & I in a long straight wire
15
! 
We can use Ampere’s law to find the magnetic field
around a long, straight wire:
∑ B ΔL = µ I
!
0 enclosed
B ( 2π r ) = µ0 I
B=
µ0 I
2π r
Clicker question: 2
16
Force between wires
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! 
The magnetic field generated by wire 1 at wire 2 is
µ 0 I1
B=
2π d
! 
The force on wire 2 is
F = I 2 LB
! 
Therefore the force per unit length on either wire is
F12 µ0 I1 I 2
=
L
2π d
d
Demo: 1
18
! 
Pinch wires
!  Parallel
hanging wires are either attracted or
repelled by one another, depending on the
directions of current in the wires.
#  Opposite
direction: repel
#  Same direction: attract
d
The magnetic field lines due to a circular current loop
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! 
! 
The magnetic field of a current loop is similar to the magnetic
field of a bar magnet.
In the center of the loop of radius R, N turns, carrying a current
I, the magnetic field is given by
N µ0 I
B=
2R
Magnetic field due to solenoid
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! 
! 
A solenoid is a helix of closely spaced turns.
The magnetic field inside a long solenoid is parallel
to its axis.
Infinite solenoid
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! 
We can use Ampere’s law to find the field inside the
infinite solenoid:
∑ B ΔL = ∑ B ΔL + ∑ B ΔL + ∑ B ΔL + ∑ B ΔL
!
!
1
!
2
= BL + 0h + 0L + 0h
= BL
∑ B ΔL = µ I
!
0 enclosed
= µ0 nLI
B = µ0 nI
n is the number of turns per unit
length.
!
3
!
4
Demo: 2
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! 
Magnetic fields around conductors
!  Visualizing
magnetic field using iron filings
Demo: 3
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! 
Electromagnet
!  A
small electromagnet powered by a 1.5V battery that
can hold several kilograms.
!  A huge coil carries up to 25A; very strong field will
attract nails, etc. that are thrown near.
Electric bells
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When a current is
applied, B field is
created, which
attracts the
clapper to the
electromagnet.
!  This breaks the
circuit, collapsing
the B field of the
electromagnet.
! 
Switch
Electromagnet
Clapper