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Ampere’s circuital law vector potential Biot - Savart. b. * Turn the compass needle so it is approximately parallel to the wire. * Close the switch to send the current through the wire for about 5-10 seconds. * The compass will align itself with the magnetic field. B. a. I. - PowerPoint PPT Presentation
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* Turn the compass needle so it is approximately parallel to the wire. * Close the switch to send the current through the wire for about 5-10 seconds. * The compass will align itself with the magnetic field.
B
Ampere’s circuital lawright hand rule
a
I
current ==> magnetic field
74 10o Henries B jo
B ds j dso
B dl j dso
B dl j dso o encB 2 I
o encI
B2
a
I
B
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B
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B2
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a
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aB
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0 < a
a
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oIB
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a
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B
oB
2
oB
2 c
a
concentric hollow cylinders
0encI 0B ( ) 1I a
( ) 2I b
( ) 1I c
a b
b c
0B
0 100 200 300 400-5
0
5
10
r
B
0-
0 a b c
B
solenoid
L
•
+
B dl j dso 2 o encLB I
2 oLB NI
o
NIB
L
we know that • B = 0vector potential A
we know that • [ x vector] = 0
we can now specify the vectorlet vector be A such that B = x A
William Thomson shows that Neumann's
electromagnetic potential A is in fact the
vector potential from which may be
obtained via B = x A.
vector potential A
we also know x B = µo j
B = x A
x x A = • A) -
- A = - µo j is similar to Poisson’s
equation but we have to solve three PDE’s
A and j are in the same direction!!
j(r’)
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Slide through the integral!
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summary
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Three techniques to find B
1] Ampere’s circuital law - lots of symmetry
2] find vector potential A, then B = x A
3] Biot - Savart law
B
A
BB
