Magnetism. • Magnetic field shapes and direction. • Fields near electric currents. •
Magnetic forces. • Moving charges and magnetism. • Magnetic machines.
Circuits revision • Here’s the circuit for the flashing neon bulb. • What is the period of the flash in seconds ?
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Magnetic Fields revision Please try problem 15 in Ch 24 on page 825. “What is the magnetic field at the center of the loop….”
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Magnetic Fields and Forces •
Magnetism
•
Magnetic field shapes and direction
•
Fields near electric currents
•
Magnetic forces
•
Moving charges and magnetism
•
Magnetic machines
•
Magnetic materials 3
Magnetism • Fundamental force of nature • Related to electricity, but not the same
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Experimental Observations • Magnetism does not move an electroscope, it does not act on stationary charges • Long range force (action over a distance) • There are 2 poles, north and south, and they come in pairs
• Like poles repel, unlike poles attract • Poles attract magnetic materials
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Magnetic Field lines • Magnetic Fields around a bar magnet • Similar to an electric dipole • Start at north pole, terminate at south pole
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Like and unlike poles Magnetic field lines between poles
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Electric Currents and Magnetic Fields Oersted found that a current can move a magnetic compass
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Direction of Magnetic field We use the right handed rule to find which way a magnetic compass would point
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Magnetic field near a loop • Bend the wire into a loop. • Dots - field is coming out of the page. • Crosses - field is going in to the page
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Field near a solenoid • Many loops will concentrate the field inside the coil • Called a solenoid – contains a uniform magnetic field
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Magnetic field due to a current Experimentally, the field strength, B, is proportional to current, I, and inversely proportional to distance, r.
0 I B 2r Units of Tesla, where μ0 is the permeability constant – 1.257x10-6 TmA-1 12
Tesla is a large unit • Magnets in the lab – 0.1 to 1 T • Kitchen magnets – 5x10-3 T • Earths magnetic field – 5x10-5 T • Superconducting magnets – in accelerators and maglev trains – 10 T
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Magnetic Field at the center of a current loop Inside a loop radius R:
B
0 I 2R 14
Magnetic Field at the center of a current loop with N turns If the loop has N turns, but its not yet a solenoid we have:
B
0 NI 2R 15
Magnetic field inside a solenoid The uniform field in a solenoid is
N B 0 I L For a solenoid with N turns, Length L and current I.
Note: independent of the coil radius. Field is uniform. 16
Magnetic Forces • The magnetic fields around two wires will attract or repel, just like bar magnets. • A magnetic field exerts a force on a current, or moving charge • Currents in the same direction attract
• Opposite currents repel 17
Direction of Magnetic Force • The force on a wire with a current is perpendicular to both the magnetic field the direction of the current. • We use another right hand rule 18
Magnitude of the Magnetic Force The force between a magnetic field and a current along a wire length L perpendicular to the field is:
F ILB 19
Magnitude of the Magnetic Force The force between a magnetic field and a current along a wire length L at an angle, α to the field is:
F ILB sin If the current and B field are parallel – there is no force.
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Force on a moving charge • A current, I, is a moving charge. • The charge q moves along the wire length L in time Δt • The velocity will be L/Δt • We find that qv=IL
L v t q qv I t L IL qv 21
Magnitude of the Magnetic Force The force between a magnetic field and a charge, q, moving with a velocity, v perpendicular to the field is:
F qvB 22
Magnitude of the Magnetic Force The force between a magnetic field and a charge, q, moving at velocity, v, at an angle, α to the field is:
F qvB sin If the moving charge and B field are parallel – there is no force. 23
Direction of Magnetic Force • The force on a moving charge is perpendicular to both the magnetic field the direction of the charge. • Note the thumb is now the direction of the +ve charge, instead of the current I. 24
Path of charges in a magnetic field • The force on a charged particle in a magnetic field is perpendicular to its direction of motion. • We always get circular or spiral paths of charged paths in a magnetic field 25
Path of charges in a magnetic field • Centripetal force of an object in a circle 2
mv F qvB r RqB v m
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Path of charges in a magnetic field • If we accelerated the ions in an electric field V, the charge to mass ratio can be measured,
1 2 E qV mv 2 q 2V 2 2 m B R
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Mass spectrometer • First measurement of e/m for the electron • Used to distinguish different types of atoms and isotopes 28
Aurora Borealis • Solar wind from the sun (protons & electrons) gets deflected by Earth’s magnetic field. • Portion of velocity perpendicular to the field lines, curves the ionizing particles into spirals • Ionize O2 and N2 in the ionosphere 29
Magnetic forces between currents • Consider two wires carrying currents I1 and I2. • The field at the top wire is I
B2
0 2
2d F12 B2 I1 L
0 LI1 I 2 F12 2d
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Magnetic forces between currents From the field from the single wire, we can deduce the force between 2 wires carrying currents I1 and I2 is
0 LI1I 2 Fparallel wires 2d 31
Torques and Magnetic Moments
• Torque was defined in chapter 7
• Quantity to measure the force applied near a pivot
• Useful for calculating rotational motion
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Torque Torque, τ, measures the effectiveness of a force at causing an object to rotate about a pivot
rF sin 33
Torque on a current loop in a B field • Current loop in a uniform field
• The forces on the top and bottom wires will rotate the loop
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Torque on a current loop in a B field • The total torque, τ, will be the sum of the torques on the top and bottom wires. • Loop height L, wire length W
L 2 F sin 2 BIWL sin
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Torque on a current loop in a B field
•In general, the torque on a loop area A will be:
IAB sin The loop is forced to align with the magnetic field
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Using torque - MRIs • Magnetic Resonance Imaging (MRI) uses the protons magnetic moment in hydrogen atoms in high 1T fields. • The rate of the emitted radio waves from the excited states are detected 37
Using Torque – Electric motor Using commutators, the loop can be made to spin, to produce rotational movement
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Permanent Magnets Ferromagnetism
• Ferromagnetism is a property of certain elements – the ability to maintain a permanent magnetic field • Depends on the crystalline structure of the metal • Found in alloys of iron, cobalt, nickel, gadolinium, dysprosium, europium • Half full electron shells, the magnetic dipole of the electrons can align 39
Periodic Table
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Crystalline structure aligned • The magnetic dipoles are grouped in micron size crystals, domains • The dipoles can be aligned by applying a magnetic field • Can be destroyed by heating (Curie point) or dropping 41
Electromagnets • An iron core near a solenoid will align the domains inside the iron • This increases the magnetic field (factor of 100) • Used to amplify the magnetic field
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Summary •
Magnetism
•
Magnetic field shapes and direction
•
Fields near electric currents
•
Magnetic forces
•
Moving charges and magnetism
•
Magnetic machines
•
Magnetic materials 43
Homework problems Chapter 24 Problems 20, 21, 31, 41, 48, 53, 56, 57
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