Post on 25-Sep-2020
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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 magneticpoles is similar to that oflike and unlike electric charges.
Law of Magnetic Poleslike 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 abar 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 materialsget "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.
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The magnetism induced in a ferromagnetic material can be very large, even with a weak external magnetic field.
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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 FmMaximum Fm Fm < Maximum
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Strength of the Magnetic Field and Force
Fm = q0 v x B
Fm = Magnetic Forceq0 = Chargev = Charge's VelocityB = Magnetic Field
Fm|q0| v sin θB =
Units: N s = 1 Tesla (T) C m
Nicola TeslaCroatianAmerican18561943
1 gauss = 104 Tesla
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Direction of the magnetic forceRight 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.
Charged particle in a magnetic field.
The electrical force can do work on acharged particle.
The magnetic force cannot do work on acharged 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 particlestarting from rest)
Substituting equation 2 into equation 1 for velocity:
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The magnetic force on themoving charges pushes thewire to the right.
The Force on a Current in a Magnetic Field
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FB = qv x B
Multiply right side by t / t.
FB = q tv x B t
Simplify:
FB = l I x B
Calculating the Force on a Current in a Magnetic Field
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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 applicationof RHR1 shows that they are opposite in direction.
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The loop tends to rotate such that its normal becomes aligned with the magnetic field.
The Torque on a CurrentCarrying Coil
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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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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.
Magnetic Fields Produced by Currents
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A LONG, STRAIGHT WIRE
Magnetic Fields Produced by Currents
B α Ir
From experiments:
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:
B = Nμ0 I2R
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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
André‐Marie Ampère1775 – 1836
French
• 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
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ΣB|| Δℓ = µo I
B|| ΣΔℓ = µo Ifactoring 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 IB (2πr) = μ0 IB = μ0 I
2πr
Ampère’s Law
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