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by: DB

Block05Notes.pdf PHYS 242

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These are notes that are going to be on the next exam.
General Physics II
Prof. Sandin
Study Guide
Engineering, General Education, General Physics, Physics
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This 2 page Study Guide was uploaded by DB on Tuesday September 27, 2016. The Study Guide belongs to PHYS 242 at North Carolina A&T State University taught by Prof. Sandin in Fall 2016. Since its upload, it has received 4 views. For similar materials see General Physics II in Physics 2 at North Carolina A&T State University.


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Date Created: 09/27/16
PHYS 242 BLOCK 5 NOTES Sections 28.1 to 28.8 → µ 0υ  × r^ µ0|q|υ sin φ Experimentally, we findB4π   2 , which has magnitude B4π  2 . r r → B  is the magnetic field (in T)causedby a moving point charge. The magnetic constant µ is defined to equal exactly 4π × 1. 0 A → m → q is its charge (in C, where 1 C≡ 1 A·s) andυ  is its constans ). Note that a nonzeroB  is in the same direction asυ  × r if the chargeq is positive, but oppositeυ  × r if the chargeq is negative. r is the distance (in m) from the source point (the point charge) to the field point.  ^ r is a unit vector directedfrom the source point to the field point. Unit vectors have no SI units but have magnitude one (unity). →  ^ φ is the angle between the directions ofυ  and r (as in Fig. 28.1a) . Cover up the solution and carefully work Example 28.1. → µ 0 dl  × r^ µ 0 dl sin φ The law of Biot and Savart, dB 4π   2 , has magnitude dB 4π   2 . Of course, to r r → → → → µ0  I dl  × r find B  , we perform the vector integral of4π ∫: Br2  . dB  is the infinitesimal magnetic field (in T)causedby a currentI (in A) flowing in an infinitesimallength → → dl  (in m) (as illustrated with a greatly exaggerated dl  in Fig. 28.3a) .  ^ r is the distance (in m) from the source point (the infinitesimallength dl) to the field point and r is the corresponding unit vector. →  ^ φ is the angle between the directions ofdl  and r . All five equations above tell us that their magnetic fields are zero boof = 0) and directly behind (φ = 180˚) a moving point charge and a bit of current. Cover up the solution and carefully work Example 28.2. µ0I Outside a long straight wire, the law of Biot andSavar2πr   , where r is the distance from the center of the wire to the field point (Roger Freedman leaves out “the center of” several times). A long straight wire’s magnetic field lines are circles centered on the wire. Mentally grasp the wire with your right hand, with your extended thumb in the direction the current flows. Your fingers then wrap around in the → directions of B  . (See Fig. 28.6.) Cover up the solutions and carefully work Examples 28.3 and 28.4 From Fig. 28.9, parallel currents attract, but antiparallel (opposite) currents repel. 2 On the axis of a flat circular coil ofN turns, the law of Biotand Savart gives  , where x 2(x  + a )/  is the distance (in m) along the axis from the center of the coil toa is the coil’s radius(in m). At µ0NI the coil’s center (that is, atx = 0), this equation reduce2a   . =  Cover up the solution and carefully work Example 28.6. → On the axis of a circular coil, the direB  is the same direction as the coil’s magneticdipole moment and area vectors: Wrap the fingers of your right hand around the coil the way the current flows. Then → your extended right thumb points along the coil’s axis in the direction of B  . → → If no magnetic materials are present,Ampere’s lawi∫ B ·d l  = 0 encl, where enclis the net constant current (in A) enclosed by the path of the integral. See use Ampere’s law in the high symmetry Examples 28.7, 28.8, 28.9, and 28.10. Delete the TEST YOUR UNDERSTANDING example on page 936 and its answeo rn page 954 because the permanent magnet is, of course, made of a magnetic material. A solenoid is a helical coil wrapped on a cylinder. When its length is much greater than its diameter, –1 Example 28.9 shows, near its center, B = µ0nI  , where n is the number of turns per length (in m ). (The chapter-opening question on page 921 and its answer on page 954 are correct only near the center of solenoids whose lengths are much greater than their diameters.) A toroidal solenoid (more commonly called a toroid) is a coil wrapped on a doughnut-shaped core. µ0NI Example 28.10 shows B =  2πr    , whereN is the number of turns (no unit)and r is the distance (in m) from the center to the field point (see Fig. 28.25). This B is the magnitude of the tangential magnetic field (in T) in the “dough” of the doughnut-shaped core (that is, within the turns). All our previous equations containi0gµ assume any materials present to be essentially nonmagnetic. The magnetic dipole moments of atoms are causedmainlyby the orbital and spin motions oftheir electrons (nuclear magnetism is about 10 times smaller). → The magnetization M  of a material is its net magnetic dipole moment per volume. Outsideof a magnet, its own magnetic field is awayfrom its N-pole and toward its S-pole. In general,this magnetic field decreases with distance from the magnet. Paramagnetismis the temperature-dependent lining up ofthe atomic magneticdipoles when placed in an external magnetic field. In the material (except at very low temperatures) paramagnetism gives oihtreaseig over the external magnetic field value. Diamagnetism is an induced effect that ordinarily gives a weak magnetization that opposes and slightly decreases the value of the external magnetic field in the material. It can be a strong effect in superconductors. In ferromagnetism, adjacent atomic magnetic dipoles line up in strong parallelism in regions called magnetic domains. In unmagnetized ferromagnetic material, those domains have random orientations. An external magnetic field causes those domains to grow and/or rotate to give a large magnetization.Figure 28.28 shows a magnetization curve for a ferromagnetic material. On the graph,0B is the component of the magnetic field that we’d have ifno materialwere present and M is the component of the magnetizationM  i0 B ’s initial direction. WhenM = M sat(where sats short fosaturationthe domains are as aligned as possible. If the domains tend to remain aligned even after the external magnetic field is removed, we have the phenomenon called hysteresis. Hysteresis gives us permanent magnets and magnetic memory materials. Figure 28.29 shows a differenthysteresis loopfor each of three applications.


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