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Unformatted text preview: Ampere's Law:
An infinite wire:
d B d = o I encl
An infinite solenoid:
3 4 2 Magnetic Materials I: Ferromagnetism
A ferromagnetic material is one in which the electronic spins are aligned in relatively large domains (~ 100 m). Examples of these material include iron and steel. I
R Bin = o nI B B= o I encl 2R Bin Toroid: Toroid: Non-uniform current density: NonJ =D r R
3 1 d When placed in a large external magnetic field, the spins, and magnetic dipole magnetic moments, of the domains all line up with the applied field. B
d R r B
d This alignment can result in large increases in the magnetic field in the field material (B ~ 1000Bo to 100000Bo). Bin between =
Monday, 19 March 2007 o NI 2r Binside r3 D 3 r = 5 R o Boutside = o I total 2r 1 Permanent magnets are made from ferromagnetic materials whose spins have spins all been fixed in one direction.
Monday, 19 March 2007 2 Magnetic Materials II: Paramagnetism
Paramagnetic materials also have net electronic spins (and thus magnetic dipole moments). They are, however, randomly oriented on an individual basis. Magnetic Materials III: Diamagnetism
Diamagnetic materials have no net electronic spin (and thus no magnetic dipole moments). Therefore, you would think that there is nothing to align to an external magnetic field. However, in the presence of a large external magnetic field, a magnetic dipole moment will be induced, or created, in such a induced, way as to oppose the external field. The net result is to reduce the magnetic field in the diamagnetic diamagnetic material by a small amount. Usually, in materials like Copper, Diamond, and Gold, B ~ 0.99995 Bo. In a perfectly diamagnetic material, like a superconductor, the magnetic field inside is ZERO! As a result, their alignment in a strong external magnetic field does not produce as large an increase in the overall magnetic field in the material (B ~ 1.00002Bo). Examples include Aluminum, Magnesium, and Tungsten. Monday, 19 March 2007 3 Monday, 19 March 2007 4 1 Recap on Magnetics
You are responsible for all of Chapter 27
Magnetic Force & Magnetic Field Big Picture Electrostatics Circuits Magnetics Chapter 27: Magnetic Force on Charges and currents Chapter 28: Sources of Magnetic Field Chapter 29: Electromagnetic Induction Chapter 30: Self Inductance and Inductors We did not, and will not, cover Section 28.1 You are responsible for the rest of Chapter 28
Source of Magnetic Field Note: The previous 3 slides are all you need to know for Section 28.8
Monday, 19 March 2007 5 Optics
Monday, 19 March 2007 6 Big New Idea: Faraday's Law Faraday' d Ed = - dt ( B dA) Previously ...
Electric Fields: q E
E= 1 q q ^ r= r 2 4 o r 4 o r 3 1 Coulomb's Law Coulomb' Electric field of a point charge! Gauss's Law Gauss' We are going to take it apart, and then put it back together again so that it will be meaningful!
Monday, 19 March 2007 7 Monday, 19 March 2007 E dA = Qencl o 8 2 Previously ...
Magnetic Fields: So ...
We had 1 way of making electric fields, 1 way of making magnetic fields, and some mathematical relationships within them. qv B
dB = ^ o Id r o Id r = 2 4 r 4 r 3 Biot-Savart Law Biot- Magnetic field of moving charges (current)! Gauss's Law Gauss' Ampere's Law Ampere'
Monday, 19 March 2007 Now ...
We are going to see a completely different way to make an electric field! It is a NEW THING that relates magnetism to electricity! electricity!
9 Monday, 19 March 2007 10 B dA = 0 B d = o I encl Demo I: Bar Magnet Demo II: Secondary Coil Monday, 19 March 2007 11 Monday, 19 March 2007 12 3 Time Varying Magnetic Field
It is not the presence of a magnetic field, but the TIME VARYING B-field that is associated with current running in the secondary coil! dB at some location in space! dt 1. Turn it on goes from 0 to some finite value 2. Constant nothing happens 3. Turn it off goes from some finite value to 0
current time Curly Electric Field
Any time at some location is space where there is a time varying B-field, in magnitude or direction, you B-field, get a pattern of E-field that we thought was impossible! If the B-field is getting weaker ... Curly E-field E- ENC ENC Non-Coulomb NonE-field B ENC Integral around a closed loop is NOT ZERO! Monday, 19 March 2007 13 Monday, 19 March 2007 E NC Ed emf
14 Faraday's Law Faraday' emf = Ed = - d dt ( B dA) = - ddt Direction
B 1. Direction of Curly E-field: EPoint your thumb in the direction opposite of the time-varying B-field, dB timeB-field, - dt then your fingers curl in the direction of the curly E-field E NC . E- The left-hand side has to do with the Curly E-field leftEThe right-hand side has to do with the Time Varying rightB-field Split the analysis of the Curly E-field into 2 parts: E1. Direction 2. Magnitude
Monday, 19 March 2007 15 Monday, 19 March 2007 16 4 Direction
1. Direction of Curly E-field: EE NC
dB dt need B t dB dt want - dB dt - t1 B1 estimate with E NC
B = Bf - Bi t2 P t1 = B2 - B1 - B1 = B2 + - B1
Monday, 19 March 2007 ( ) B2
dB dt dB - dt B1 At the origin, what is the direction of B ? A. +x E. Zero magnitude B. -x C. +y D. -y B 17 Monday, 19 March 2007 18 Question
The magnet is moving in the +z direction, away from the coil. At the origin (inside the coil), what is the direction of dB ? Question - dt The magnet is moving in the +z direction, away from the coil. At a location A on the y-axis (inside the coil), what is ythe direction of E NC ? A. +x B. -x C. +y D. -y E. Zero magnitude A. +x B. -x C. +z D. -z
Monday, 19 March 2007 E. Zero magnitude 19 Monday, 19 March 2007 20 5 ...
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This note was uploaded on 04/08/2008 for the course PHGN 200 taught by Professor Japguy during the Fall '07 term at Mines.
- Fall '07