•here’s the circuit for the flashing neon bulb. what is ... · pdf file•...
TRANSCRIPT
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1
Circuits revision
• Here’s the circuit for the flashing neon bulb.
• What is the period of the flash in seconds ?
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2
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
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4
Magnetism
• Fundamental force of nature
• Related to electricity, but not the same
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5
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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8
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.
Units of Tesla, where μ0 is the permeability constant – 1.257x10-6 TmA-1
r
IB
2
0
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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:
R
IB
2
0
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15
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:
R
NIB
2
0
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Magnetic field inside a solenoid
The uniform field in a solenoid is
For a solenoid with N turns, Length L and current I.
Note: independent of the coil radius. Field is uniform.
L
NIB 0
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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
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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
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Magnitude of the Magnetic Force
The force between a magnetic field and a current along a wire length L perpendicular to the field is:
ILBF
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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:
If the current and B field are parallel – there is no force.
sinILBF
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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 qvIL
L
qv
t
qI
t
Lv
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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:
qvBF
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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:
If the moving charge and B field are parallel – there is no force.
sinqvBF
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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.
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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
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Path of charges in a magnetic field
• Centripetal force of an object in a circle
m
RqBv
qvBr
mvF
2
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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,
22
2
2
2
1
RB
V
m
q
mvqVE
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Mass spectrometer
• First measurement of e/m for the electron
• Used to distinguish different types of atoms and isotopes
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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
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Magnetic forces between currents
• Consider two wires carrying currents I1 and I2.
• The field at the top wire is
d
ILIF
LIBF
d
IB
2
2
21012
1212
202
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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
d
ILIF wiresparallel
2
210
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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
sinrF
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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
sin
sin2
2
BIWL
LF
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Torque on a current loop in a B field
•In general, the torque on a loop area A will be:
The loop is forced to align with the magnetic field
sinIAB
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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
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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
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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
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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
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Homework problems
Chapter 24 Problems
20, 21, 31, 41, 48, 53, 56, 57