2 Exam covers Ch. 27-32, Lecture, Discussion, HW, Lab
Exam 2 is Wed. Mar. 26, 5:30-7 pm, 2103 Ch: Adam(301,310), Eli(302,311), Stephen(303,306), 180 Science Hall: Amanda(305,307), Mike(304,309), Ye(308)
Electric current produces magnetic field
Current (flow of electric charges ) in wire produces magnetic field. That magnetic field aligns compass needle
Current
Chapter 27: Electric flux & Gauss law Chapter 29: Electric potential & work Chapter 30: Electric potential & field Chapter 28: Current & Conductivity Chapter 31: Circuits Chapter 32: Magnetic fields & forces
(exclude 32.6,32.8,32.10)
Physics 208, Lecture 17 1 Wed. Mar. 26, 2008 Physics 208, Lecture 17
Magnetic field
2
Wed. Mar. 26, 2008
Law of Biot-Savart
B out of page r
ds
I
Each element of current produces a contribution to the magnetic field.
dB
Magnetic field from long straight wire: Direction
r Idr # r s dB = o 4" r 2
y
dI
r
dB =
Wed. Mar. 26, 2008 Physics 208, Lecture 17
o Ids # r 4" r 2
3
What direction is ! the magnetic field from an infinitely-long straight wire?
x I
Wed. Mar. 26, 2008
Physics 208, Lecture 17
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!
Current dependence
How does the magnitude of the B-field change if the current is doubled?
A) Is halved B) Quadruples C) Stays same D) Doubles E) Is quartered
r Idr # r s dB = o 4" r 2
y
r Distance dependence dB = o Ids 2# r
How does the magnitude of the B-field at 2 compare to that at 1?
A) B2=B1 B) B2=2B1
r
4"
r
2
y
!
x I
!
1 x I
C) B2=B1/2 D) B2=4B1 E) B2=B1/4
Wed. Mar. 26, 2008
Physics 208, Lecture 17
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Wed. Mar. 26, 2008
Physics 208, Lecture 17
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1
Why?
r Idr # r s Biot-Savart says dB = o 4" r 2
Why B(r) 1/r instead of 1/r2 ?
Large contribution from this current element. Decreases as 1/r2
Long straight wire
All current elements produce B out of page
o 4" = o 4" = o 4"
Ids # r r2 I sin $ r2 I a o a = I r 2 r 4" ( x 2 + a2 )3 / 2
dB =
Add them all up:
B=
Small contribution from this current ! element. ~ independent of r
o Ia $ dx I = o % 4 " #$ ( x 2 + a 2 ) 3 / 2 2"a
a !
!
r
r r
I
r = x 2 + a2
!
Wed. Mar. 26, 2008
x
8
!
Physics 208, Lecture 17
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Wed. Mar. 26, 2008
Physics 208, Lecture 17
Forces between currents
Which of these pairs of currents will attract each other?
A. B. C. D.
Force between current-carrying wires
A A&C B A&B
Attractive for parallel currents. Repulsive for antiparallel currents
A
B
C
Wed. Mar. 26, 2008
Physics Lecture 208, 17
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Wed. Mar. 26, 2008
Physics 208, Lecture 17
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Field from a circular loop
Magnetic field from loop
Which of these graphs best represents the magnetic field on the axis of the loop? y x z C. A.
Bz z Bz
Each current element produce dB All contributions add as vectors Along axis, all components cancel except for x-comp
B. Bz
z
z Bz
D. z
Wed. Mar. 26, 2008 Physics 208, Lecture 17 11 Wed. Mar. 26, 2008 Physics 208, Lecture 17 12
2
Magnetic field from a current loop
Solenoid electromagnet
Sequence of current loops can produce strong magnetic fields. This is an electromagnet
One loop: field still loops around the wire.
Many loops: same effect
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Physics 208, Lecture 17
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Wed. Mar. 26, 2008
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Comparing Electric, Magnetic
A shortcut: Amperes law
Biot-Savart: calculate B-field from current distribution.
Resulting B-field is a vector, and complication: current (source) is a vector!
Integral around closed path proportional to current passing through any surface bounded by path.
!
Amperes law
" B ds = I
o
I
closed path surface bounded by path
Coulomb: calculate E-field from charge distribution
Right-hand rule:
Resulting E is a vector but charge (source) is not a vector
Thumb in direction of positive current Curled fingers show direction integration
Physics 208, Lecture 17
Wed. Mar. 26, 2008
Physics 208, Lecture 17
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Testing Amperes law
Using Amperes law...