My lecture slides are posted at Information for Physics 112 midterm, Wednesday, May 2


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1 My lecture slides are posted at Information for Physics 112 midterm, Wednesday, May 2 1) Format: 10 multiple choice questions (each worth 5 points) and two showwork problems (each worth 25 points), giving 100 points total. 2) Closed book and closed notes. 3) Can make up your own equation sheet on a single normal sized piece of paper (8.5 x 11"), both sides of sheet  handwritten  no worked out problems  only equations and physical constants allowed  signed equation sheet must be turned in with the exam 4) Covers the material in Chapters 18, 19, 20 Electricity only
2 Chapter 21 Magnetic Forces and Magnetic Fields
3 Currents in wires produce magnetic fields. The long currentcarrying vertical wire shown will cause a compass needle to deflect in a circular pattern around the wire in a horizontal plane. 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.
4 The magnitude of the Bfield created from a long, straight wire carrying current I at a distance r from the wire is found experimentally to be, µ o B = I 2π r µ o = 4π 10 7 T m A Why must the wire be long? è to avoid fringe field effects. permeability of free space
5 Example 7 A Current Exerts a Magnetic Force on a Moving Charge The long straight wire carries a current of 3.0 A. A particle has a charge of +6.5x106 C and is moving parallel to the wire at a distance of m. The speed of the particle is 280 m/s. Determine the magnitude and direction of the magnetic force on the particle.
6 µ B oi 2π r = Magnetic field at a distance r from the wire with current I Force on a moving charge in a Bfield, F = sin ( µ θ sinθ 2π # % oi qvb = qv & ' r $ = (6.5 x 106 )(280) {(4π x 107 )(3.0)/[2π(0.050)]} sin 90 o = 2.2 x 108 N From RHR2 (for B) and RHR1 (for F), F is radially inward.
7 Current carrying wires can exert forces on each other. currents in opposite directions currents in same direction Calculate the magnitude of the force on Wire 2 due to Wire 1, F 21, if the wires carry currents I 1 and I 2, respectively, and are separated by a distance r. F 21 = I 2 LB 21 sin θ where B 21 = µ 0 I 1 /(2πr) is the Bfield at 2 from 1 F 21 = I 2 L{µ 0 I 1 /(2πr)}sin θ = I 1 L{µ 0 I 2 /(2πr)}sin θ = F 12, the force on 1 by 2 Using RHR1 and RHR2 this agrees with Newton s 3rd law that F 12 =  F 21
8 Conceptual Example 9 The Net Force That a CurrentCarrying Wire Exerts on a Current Carrying Coil Is the coil attracted to, or repelled by the wire? è answer: attracted to (why?) B 1 (in)
9 The magnetic field at the center of a loop of wire of radius R with current I is found to be experimentally, µ B = oi 2R center of circular loop Find the direction of the Bfield at the center by using RHR2.
10 Example 10 Finding the Net Magnetic Field A long straight wire carries a current of 8.0 A and a circular loop of wire carries a current of 2.0 A and has a radius of m. The wires are adjacent to each other without touching. Find the magnitude and direction of the magnetic field at the center of the loop.
11 B = B 1(straight wire) + B 2(loop) B = µ I & 1 µ oi 2 µ o I1 = $ 2π r 2R 2 % π r I R o 2 #! " B = ( 7 π 10 T m A) 4 ( 8.0 A 2.0 A % T 2 & = ( m) m # ' π $ Since B 1 > B 2, the direction of B is along B 1, normal to the current plane.
12 The field lines around the bar magnet resemble those around the loop. To find the direction of the phantom North Pole of a loop, use RHR2 and the direction of B at the center is also the direction of the North Pole.
13 Loop currents in the same direction, phantom magnets attract. Loop currents in opposite directions, phantom magnets repel. è similar behavior as two parallel currentcarrying wires.
14 A solenoid is made up of many current loops which extend a finite distance along the axis of the loops characterized by the number of turns (number of loops) per unit length, n. The Bfield in the interior of a long solenoid depends only on n and the current in the loops, I, as B = µ ni o Interior of a long solenoid (B ~ 0 outside) Use RHR2 for direction of B inside Bfield lines similar to those of a bar magnet with N and S poles shown.
15 21.8 Ampere s Law AMPERE S LAW FOR STATIC MAGNETIC FIELDS For any current geometry that produces a magnetic field that does not change in time, sum up all of the segment lengths Δl multiplied by the B è this equals a constant multiplied by the current enclosed by the path. In mathematical notation, B Δ = µ oi net current passing through surface bounded by path Note: this is a messy thing to use for anything except in situations where the geometry of the problem has a lot of symmetry, e.g. the long straight wire
16 21.8 Ampere s Law Example 11 An Infinitely Long, Straight, CurrentCarrying Wire Use Ampere s law to obtain the magnetic field è lots of symmetry! B Δ = µ I o Can choose a path where B is constant B ( Δ ) = µ I o Since path is a circle of radius r B2π r = µ I o On RHS, I is the only current enclosed by path µ B oi 2π r = è We get our familiar equation!
17 21.9 Magnetic Materials The intrinsic spin and orbital motion of electrons gives rise to the magnetic properties of materials è electron spin and orbits act as tiny current loops. In ferromagnetic materials groups of neighboring atoms form magnetic domains where the spins of electrons are naturally aligned with each other; magnetic domain sizes are ~ mm. An external magnetic field can induce magnetism in ferromagnetic materials by merging and aligning domains. Depending on the material, the induced magnetism may or may not become permanent. Putting iron in the center of a solenoid can create a strong electromagnet with fields 100x x the applied fields (also, can turn fields on and off).
18 21.9 Magnetic Materials Magnetic tape recording. The induced magnetization patterns on the magnetic coating become permanent so the recording can be played back later.
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