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Unit 9­Magnetism
This end points to the North;
call it "NORTH."
This end points to the South;
call it "SOUTH."
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The behavior of magnetic
poles is similar to that of
like and unlike electric charges.
Law of Magnetic Poles
like poles repel, and unlike poles attract
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Magnetic Field (B)
altered region in space around a magnet where the magnet's influence can be felt
The direction of the magnetic field at any point in space is the direction indicated by the north pole of a small compass needle placed at that point.
http://phet.colorado.edu/en/simulation/magnet­and­compass
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The magnetic field lines and pattern of iron filings in the vicinity of a
bar magnet and the magnetic field lines in the gap of a horseshoe magnet.
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What about atoms makes them magnets?
Unpaired electrons both orbit and spin, producing a mini­magnet in each atom.
Most materials have random alignment of these atoms, but ferromagnetic materials
get "huge" (0.01­0.1 mm across chunks (called magnetic domains) all aligned with each other.
Induced magnetism comes about for two reasons:
1. domains close to the orientation of the external magnetic field grow in size at the expense of the other domains. 2. some domains rotate and become more oriented in the direction of the magnetic field. 5
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The magnetism induced in a ferromagnetic material can be very large, even with a weak external magnetic field. 6
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Magnetic Fields and Moving Charges
Charges in electric fields experience electric forces.
Charges in magnetic fields MIGHT experience magnetic forces. 1. The charge must be moving.
2. The velocity of the moving charge must have a component perpendicular to the direction of the magnetic field. No Fm
Maximum Fm
Fm < Maximum
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Strength of the Magnetic Field and Force
B =
Fm
|q0| v sin θ
Fm = Magnetic Force
q0 = Charge
v = Charge's Velocity
B = Magnetic Field
Fm = q0 v x B
Units: N s = 1 Tesla (T)
C m
Nicola Tesla
Croatian­American
1856­1943
1 gauss = 10­4 Tesla
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Direction of the magnetic force
Right hand rule #1 for magnetism:
1. Right thumb points in the direction of the velocity.
2. Right fingers point in the direction of the magnetic field.
3. Right palm pushes in the direction of the magnetic force.
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The Motion of a Charged Particle in a Magnetic Field
Charged particle in an electric field.
The electrical force can do work on a
charged particle.
Charged particle in a magnetic field.
The magnetic force cannot do work on a
charged particle.
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The magnetic force always remains perpendicular to the velocity and is directed toward the center of the circular path.
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The Mass Spectrometer
• identifies unknown molecules in chemical reactions
• give anesthesiologists information on the gasses in the patient's lungs
(for a singly ionized particle
starting from rest)
Substituting equation 2 into equation 1 for velocity:
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The Force on a Current in a Magnetic Field
The magnetic force on the
moving charges pushes the
wire to the right.
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Calculating the Force on a Current in a Magnetic Field
FB = qv x B
Multiply right side by t / t.
FB = q tv x B
t
Simplify:
FB = l I x B
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What are the top and bottom forces producing?
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The Torque on a Current­Carrying Coil
The two forces on the loop have equal magnitude but an application
of RHR­1 shows that they are opposite in direction.
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The Torque on a Current­Carrying Coil
The loop tends to rotate such that its normal becomes aligned with the magnetic field.
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Calculating the Torque on a Current­Carrying Coil
N = number of coils
NIA = magnetic moment (in A m2)
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Magnetic Fields Produced by Currents
A current carrying wire experiences a magnetic force when it is in a magnetic field.
But, a current carrying wire also produces a magnetic field of its own!
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Magnetic Fields Produced by Currents
Right­Hand Rule No. 2. Curl the fingers of the right hand into the shape of a half­circle. Point the thumb in the direction of the conventional current, and the tips of the fingers will point in the direction of the magnetic field.
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Magnetic Fields Produced by Currents
A LONG, STRAIGHT WIRE
From experiments: I
B α r
μ0 = Permeability of Free Space
= 4π x 10-7 T m/A
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Magnetic Fields Produced by Currents
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Magnetic Fields Produced by Currents
MAGNETIC FIELD PRODUCED BY A LOOP OF WIRE
If you have multiple (N) loops:
μ0 I
B = N 2R
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53. A long solenoid has 1400 turns per meter of length, and it carries a current of 3.5 A small circular coil of wire is placed inside the solenoid with the normal to the coil oriented at an angle of with respect to the axis of the solenoid. The coil consists of 50 turns, has an area of 1.2 x 10­3 m2, and carries a current of 0.50 A. Find the torque exerted on the coil.
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56. Two long, straight wires are separated by 0.120 m. The wires carry currents of 8.0 A in opposite directions, as the drawing indicates. Find the magnitude of the net magnetic field at the points labeled A and B.
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Ampère’s Law
• Ampère found a procedure for deriving the relationship between the current in an arbitrarily shaped wire and the magnetic field produced by the wire.
• Ampère’s Circuital Law
• ΣB|| Δℓ = µo I
• Sum over the closed path
André‐Marie Ampère
1775 – 1836
French
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Ampère’s Law
ΣB|| Δℓ = µo I
B|| ΣΔℓ = µo I
factoring out B since it is the same for all elements
B|| ΣΔℓ = µo I
distance around the shape
For a circle:
B is always perpendicular to radius (parallel to tangent)
B|| = B
B Σ Δ l = μ0 I
B (2πr) = μ0 I
B = μ0 I
2πr
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