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Ampere’s Law
±
Ampere’s Law
states that the line
integral of
around any closed
path
equals
μ
o
I where I is the total
steady current passing through any
surface bounded by the closed path
o
dI
μ
⋅=
∫
Bs
r
r
±
d
⋅
r
r
d
s
r
d
⋅
r
r
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View Full Document Ampere’s Law, cont
±
Ampere’s Law describes the creation of magnetic
fields by all continuous current configurations
±
Most useful for this course if the current configuration
has a high degree of symmetry
±
Put the thumb of your right hand in the direction of
the current through the amperian loop and your
figures curl in the direction you should integrate
around the loop
d
⋅
Bs
r
r
Amperian Loops
±
Each portion of the path satisfies one or
more of the following conditions:
±
The value of the magnetic field can be argued
by symmetry to be constant over the portion of
the path
±
The dot product can be expressed as a simple
algebraic product B ds
±
The vectors are parallel
d
⋅
Bs
r
r
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View Full Document Amperian Loops, cont
±
Conditions:
±
The dot product is zero
±
The vectors are perpendicular
±
The magnetic field can be argued to be
zero at all points on the portion of the path
d
⋅
Bs
r
r
Field Due to a Long Straight
Wire – From Ampere’s Law
±
Want to calculate
the magnetic field at
a distance
r
from the
center of a wire
carrying a steady
current
I
±
The current is
uniformly distributed
through the cross
section of the wire
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View Full Document Field Due to a Long Straight Wire
– Results From Ampere’s Law
±
Outside of the wire,
r
>
R
±
Inside the wire, we need I’, the current
inside the amperian circle
(2
)
2
o
o
dBr
I
I
B
r
π
μ
⋅=
=
=
∫
Bs
r
r
±
2
2
2
)
'
'
2
o
o
r
I
I
I
R
I
Br
R
πμ
=
=
⎛⎞
=
⎜⎟
⎝⎠
∫
r
r
±
Field Due to a Long Straight Wire
– Results Summary
±
The field is
proportional to
r
inside the wire
±
The field varies as
1/
r
outside the wire
±
Both equations are
equal at
r
=
R
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This note was uploaded on 06/02/2008 for the course PHYS 102 taught by Professor N/a during the Spring '08 term at Drexel.
 Spring '08
 N/A
 Physics, Current

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