SMU PHYS 1308 - Magnetic Force between Currents

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no tagsLecture 017: Magnetic Force between CurrentsYourName, 1 April 2011 (created 1 April 2011)Goals of these lectures:Discuss the implications of moving charge creating magnetic fieldsExercise: calculate the scale (order of magnitude) of terrestrialmagnetism using the Bohr model of the atomLoops of current exposed to magnetic field: dipoles and motorsIntroduce and Discuss Ampere's LawReview from last timeWe discussed two application of the Biot-Savart Law, a law which allows youto determine the magnetic field created by a moving electric charge (orcharges). We obtained two results from that effort:The magnetic field around a current-carrying wire:where is your distance from the wire. The magnetic field CIRCULATESaround the wire, perpendicular both to the current AND the line fromthe current to where you measure the field.The magnetic field along the central axis of a current-carrying loop: thisis the simplest circuit, and the magnetic field along the central axis ofsuch a loop isGeneral Physics - E&M (PHY 1308) LectureNotesGeneral Physics - E&M (PHY 1308) LectureNotesjBj ~=Ö I02Ùyy \oint ds = 2 \piGeneral Physics - E&M (PHY 1308) - Lecture Notes file:///home/sekula/Dropbox/Documents/Notebook...1 of 4 04/05/2011 08:41 AMjBjwhere is the radius of the loop and is the distance from then centerof the loop along the axis. This is just like the dipole electric field alongthe bisecting axis of an electric dipole; in fact, a current loop, thesimplest circuit, is just a magnetic dipole with a dipole field.When you are VERY FAR from the center of the current loop, so that theloop appears tiny compared to the distance from the loop ( ), the aboveequation simplifies to:Magnetic attraction of two wiresWhat if you place two parallel lines of current next to one another,separated by a distance ? Since each wire emits a magnetic field, and weknow that moving charge RESPONDS to magnetic field by feeling a force,something must happen. Force causes motion.We know from the last lecture that the magnetic field emitted by current 1at the location of current 2, a distance away, will be:BWe determined this from the Biot-Savart Law (BSL).Let us define the currents to flow along the x-axis in the direction . Themagnetic field from current 1 will point UP at the location of current 2; thusit points in the direction. Current 2 also flows in the positive direction(x-direction) so by construction current 2 and the magnetic field fromcurrent 1 are perpendicular and~=Ö2(x )2+ a2 3=2a x x > > ajBj ~=2x3Ö Ia02d d 1=2ÙdÖ I0 1i ^+j ^i ^I L L B (i ) L B k 2 2~Â B1~= I2 2 1^Â j^= I2 2 1^RGeneral Physics - E&M (PHY 1308) - Lecture Notes file:///home/sekula/Dropbox/Documents/Notebook...2 of 4 04/05/2011 08:41 AMand we immediately know the direction of the force on current 2 due tocurrent 1: it pulls current 2 in the positive z direction, TOWARD current 1.The magnitude of the force is just:F L B LIf you then ask what force the magnetic field from current 2 exerts oncurrent 1 we have only to recognize that at current 1's location, themagnetic field from current 2 points DOWN and thus:and substituting with the equation for from the Biot-Savart Law:and current 2 also pulls current 1 toward it.If the currents point in the same direction, the force between them isattractive. If they point in opposite directions, it's repulsive.This force can be QUITE LARGE for large currents. Engineers have to worryabout this force when designing electricity transport systems, like powerlines or transformers (which contain many close coils of wire with highcurrent in them). The hum or buzzing you often hear near high-currentdevices is due to the vibration from this magnetic force, as the current insuch devices alternates (changes direction and magnitude) and thus theforce changes in strength at about 120 times per second (120Hz).SHOW THE MIT VIDEO OF TWO WIRES WITH CURRENT FLOWING INTHE SAME OR OPPOSITE DIRECTIONS.12= I2 2 1= I2 22ÙdÖ I0 1=2ÙdÖ I I L0 1 2 2F L L B (i j) L B (Àk) 21~= I1 1~Â B2~= I1 1 2^Â À^= I1 1 2^B 2F (Àk) 21~=2ÙdÖ I I L0 2 1 1^General Physics - E&M (PHY 1308) - Lecture Notes file:///home/sekula/Dropbox/Documents/Notebook...3 of 4 04/05/2011 08:41 AMClass Exercise: Collaborate to Calculate the Scale ofTerrestrial MagnetismFollow the worksheet on this exercise.General Physics - E&M (PHY 1308) - Lecture Notes file:///home/sekula/Dropbox/Documents/Notebook...4 of 4 04/05/2011 08:41


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