This preview shows page 1. Sign up to view the full content.
Unformatted text preview: Magnetic Field
A compass needle turns and points in a particular direction ... there is something which interacts with it Magnetic field (B): whatever it is that is detected by a compass Compass: similar to electric dipole Magnetic fields are produced by moving charges Current in a wire: convenient source of magnetic field The electron current (i) is the number of electrons per second that enter a section of a conductor. The Magnetic Effects of Currents
Conclusions: The magnitude of B depends on the amount of current A wire with no current produces no B B is perpendicular to the direction of current B under the wire is opposite to B over the wire Oersted effect: discovered in 1820 by H. Ch. rsted How does the field around a wire look like? Hans Christian rsted (1777  1851) The Magnetic Effects of Currents The moving electrons in a wire create a magnetic field Principle of superposition: Bnet = BEarth + Bwire What can you say about the magnitudes of BEarth and Bwire? What if BEarth were much larger than Bwire? Exercise
A currentcarrying wire is oriented NS and laid on top of a compass. The compass needle points 27o west. What is the magnitude and direction of the magnetic field created by the wire Bwire if the magnetic field of Earth is BEarth= 2 105 T (tesla). Bnet = BEarth + Bwire Bwire = BEarth tan Bwire = 2 105 T tan 27 Bwire 1 105 T BiotSavart Law for a Single Charge Electric field of a point charge: E = 1 q ^ r 2 4 0 r Moving charge makes a curly magnetic field: B units: T (tesla) = kg s2A1 0 qv r ^ B= 4 r 2 0 T m2 = 107 4 C m/s JeanBaptiste Biot (17741862) Felix Savart (17911841) Nikola Tesla (18561943) Nikola Tesla (18561943)
High tension coil demonstration The Cross Product
Calculate cross product (vector): Ax Bx Ay Bz  Az By A B = A y By = Az Bx  Ax Bz A B A B  A B z z x y y x Calculate magnitude: A B = A B sin Calculate direction: Righthand rule 0 qv r ^ B= 4 r 2 Twodimensional Projections a vector (arrow) is facing into the screen a vector (arrow) is facing out of the screen 0 qv r ^ B= 4 r 2 B B r v B B B Exercise 0 qv r ^ B= 4 r 2 What is B straight ahead? What if the charge is negative? Exercise
What is the magnetic field created by an electron spinning around the nucleus in the simple Bohr model of the H atom? v = 2.2106 m/s r = 0.51010 m v 0 qv r ^ B= 4 r 2 r 0 qv B= sin 2 4 r
2 1.6 10 19 C 2.2 10 6 m/s 7 T m B = 10 sin 2 10 C m/s 2 0.5 10 m ( ( )( ) ) B = 14 T (BEarth=2105 T) Distance Dependence
B2 0 qv r ^ B= 4 r 2 r B1 v B3 0 qv B= sin 2 4 r Which of the B1 and B2 is larger? Which of the B2 and B3 is larger? Moving Charge Sign Dependence 0 qv r ^ B= 4 r 2
r B1 v 0 qv B= sin 2 4 r
Magnetic field depends on qv: Positive and negative charges produce the same B if moving in opposite directions at the same speed For the purpose of predicting B we can describe current flow in terms of `conventional current' positive moving charges. r B v B1 r v Exercise
A currentcarrying wire lies on top of a compass. What is the direction of the electron current in this wire? Find out experimentally from which end of the battery electrons emerge? What is the direction of conventional current? Frame of Reference
Electric fields: produced by charges Magnetic fields: produced by moving charges Any magnetic field? 0 qv r ^ B= =0 4 r 2 0 qv r ^ B= 0 2 4 r charged tape Frame of Reference 0 qv r ^ B= 4 r 2
Must use the velocities of the charges as you observe them in your reference frame! There is a deep connection between electric field and magnetic fields (Einstein's special theory of relativity) Retardation
If we suddenly change the current in a wire: Magnetic field will not change instantaneously. Electron and positron collide: Produce both electric and magnetic field, these fields exist even after annihilation. Changes propagate at speed of light 0 qv r ^ B= 4 r 2 There is no time in BiotSavart law: Speed of moving charges must be small Electron Current
To observe magnetic fields: need to produce steady flow of charges in one direction Need to find a way to produce and sustain E in a wire Use battery Electron Current m electrons 2 n A m v ( t s ) = nAv t electrons 3 s m ( ) mobile electron density wire Cross sectional area Average drift speed # electrons = nAv Electron current: i = s Typical Mobile Electron Density
Example: copper wire (Cu) Molar mass = 64 g Density = 9 g/cm3 = 9.103 kg/m3 Each atom gives one electron 0.064 kg 1.07 1025 kg Mass of one atom: mCu 6 1023
Number of atoms in 1 m3: 9 103 kg/m3 n 8.4 1028 m3 1.07 1025 kg Typical Mobile Electron Drift Speed
Typical electron current in a circuit is ~ 1018 electrons/s. What is the drift speed of an electron in a 1 mm thick copper wire of circular cross section? # electrons = nAv s
2 n 8.4 1028 m3
3 2 3.14 (1 10 m ) D A= = 8 10 7 m 2 4 4
1018 s1 1018 s1 v= = 1.5 10 5 m/s nA 8.4 10 28 m 3 8 10 7 m 2 ( )( ) Typical Mobile Electron Drift Speed
Typical electron current in a circuit is 1018 electrons/s. What is the drift speed of an electron in a 1 mm thick copper wire? n 8.4 1028 m3 v = 1.5 105 m/s
How much time would it take for a particular electron to move through a piece of wire 30 cm long? s 0.3 m t= = = 2 104 s 5.5 hours! v 1.5 105 m/s
How can a lamp light up as soon as you turn it on? Conventional Current
In some materials current moving charges are positive: Ionic solution "Holes" in some materials (same charge as electron but +) Observing magnetic field around copper wire: Can we tell whether the current consists of electrons or positive `holes'? 0 qv r 0 ev r ^ ^ ^ 0 ( e) (  v ) r B= B= = 2 2 4 r 4 r 4 r2 The prediction of the BiotSavart law is exactly the same in either case. Conventional Current 0 ev r ^ ^ 0 ( e) (  v ) r B= = 2 4 r 4 r2
Metals: current consists of electrons Semiconductors: ntype electrons ptype positive holes Most effects are insensitive to the sign of mobile charges: introduce conventional current: I = q i = q nAv
Units: C/s A (Ampere)
Andr Marie Ampre (1775  1836) Exercise
A typical electron current in a circuit is 1018 electrons/s. What is the conventional current? I = q i = 1.6 10 19 C 1018 s1 = 0.16 A ( )( ) ...
View
Full
Document
This note was uploaded on 04/02/2008 for the course PHYS 272 taught by Professor K during the Winter '07 term at Purdue UniversityWest Lafayette.
 Winter '07
 k

Click to edit the document details