Sources of Magnetic Field

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Sources of Magnetic Field What are some sources
of Magnetic Field?
Current Elements (Biot-Savart Law)
Moving Point Charges
(CH 27, 23)
Direction from RHR I
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Sources of Magnetic Field
Electric dipole
Magnets (magnetic dipole moment m)
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Exercise Compass and B-Field
Magnetic dipole moment m
Take your compass and place it flat on your
table. The compass needle will lie along the
direction of the total local magnetic field. Hold
your cylindrical bar magnet so its axis is
perpendicular to the compass needle and it is in
the plane of the compass (see figure). Hold
magnet far from the compass to start. Slowly
bring it closer to the compass and observe the
needle deflection.
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Magnetic field along axis, distance x away from
center
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Biot-Savart and RHR The Biot-Savart Law is A
small piece of a current carrying wire lying
along the y-axis is indicated on the sketches.
? P1 (0,y1)
P2 (x1,0)
P3 (x3,0)
(0,y)
a) What is the direction of the magnetic field
at the point P1? b) What is the direction of
the magnetic field at the point P2? c) What is
the direction of the magnetic field at the point
P3?
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More Biot-Savart A long straight current
carrying wire, length 2L, is oriented along the
y-axis as shown. A small piece of the wire at
(0,y) is indicated. A field point P is on the
x-axis at a distance xP. What is ?
What is ?
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Example Biot-Savart Applied to Long Straight
Wire
L
P (xp,0)
(0,y)
-L
Note points into page as expected
Limits of integration from sketch smallest
y-value for wire is L, highest y-value for wire
is L.
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Magnetic Field from Straight Wire On
bisector Infinite wire take limit as
Direction Magnetic field makes closed circles
around wire. RHR applied to straight wires
Point thumb in current direction fingers curl
in direction of magnetic field.
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Exercise Magnetic Field from Wires

• Take your compass and place it flat on your desk
  or notebook.
• The compass needle will lie along the direction
  of the total local magnetic field.
• Take out your batteries/pack and an alligator
  clip lead (or several).
• Lay the a length of wire on top of the compass so
  that the wire is parallel to the needle (dont
  complete circuit yet.
• Arrange so that the current in the wire will flow
  from south to north (north should point towards
  the front of the room). Dont complete circuit
  yet.
• Use RHR to PREDICT the direction the needle
  should deflect.
• Check your prediction.

• Repeat, but this time with wire beneath compass.
• Repeat, but this time with wire perpendicular to
  compass needle. Try both above and below the
  compass.

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ConcepTest 15 Two long straight wires each
carry the same current and are the same distance
from the origin. For the wire on the y-axis, the
current goes into the page, and for the wire on
the x-axis, the current comes out of the page, as
shown. Consider the following directions. Hold
up as many cards as you need to specify the
direction. What is the direction of the net
magnetic field at the origin?
Use formula to get magnitude of B Use RHR to get
direction of B DRAW vectors Add VECTORS!
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ConcepTest 16 Wire 1 carries current I
going up as shown. Wire 2 is a distance d away
from wire 1, and carries current I going down as
shown. Consider the following directions. Hold
up as many cards as you need to specify the
direction.

• What is the direction of the magnetic field at
  the location of wire 2 due to the current in wire
  1?
• b) What is the direction of the magnetic force
  acting on wire 2 due to the magnetic field from
  wire 1?

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Example Biot-Savart Applied to Circular Arc (at
center of arc)
RHR applied to arcs or loops of current at center
of arc or loop Curl fingers in current
direction thumb points in magnetic field
direction.
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Biot-Savart Applied to Circular Arc (at
center of arc)
Direction Magnetic field perpendicular to plane
of loop. RHR applied to arcs or loops Curl
fingers in current direction, thumb points in
direction of magnetic field.
Circular Loop at center of loop
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Example Biot-Savart Applied to Circular Loops
(on axis of loop)
Direction Magnetic field along axis of
loop. RHR applied to loops Curl fingers in
current direction, thumb points in direction of
magnetic field.
Note resemblance to field from magnetic moment!
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Equivalence of Current Loops and Bar Magnets
MAGNETIC MOMENTS
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Magnetic Field of Special Current Configurations