Magnetic Fields
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Magnetic Fields
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Lecture Notes
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 School:
 Massachusetts Institute of Technology
 Course:
 8 02t  Electricity and Magnetism
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Unformatted text preview:
Summary of Class 15 8 02 Wednesday 3 9 05 Thursday 3 10 05 Topics Magnetic Fields Creating Magnetic Fields Biot Savart Related Reading Course Notes Liao et al Sections 9 1 9 2 Serway and Jewett Sections 30 1 30 2 Giancoli Sections 28 1 28 3 Experiments 6 Magnetic Force on Current Carrying Wires Topic Introduction Last class we focused on the forces that moving charges feel when in a magnetic field Today we will extend this to currents in wires and then discuss how moving charges and currents can also create magnetic fields The presentation is analogous to our discussion of charges creating electric fields We first describe the magnetic field generated by a single charge and then proceed to collections of moving charges currents the fields from which we will calculate using superposition just like for continuous charge distributions Lorenz Force on Currents Since a current is nothing more than moving charges a current carrying wire will also feel a G G G force when placed in a magnetic field F IL B where I is the current and L is a vector pointing along the axis of the wire with magnitude equal to the length of the wire Field from a Single Moving Charge Just as a single electric charge creates an electric field which is proportional to charge q and falls off as r 2 a single moving electric charge additionally creates a magnetic field given by G q vG x r B o 4 r 2 Note the similarity to Coulomb s law for the electric field the field is proportional to the charge q obeys an inverse square law in r and depends on a constant the permeability of free space 0 4 x 10 7 T m A The difference is that the field no longer points along r but is instead perpendicular to it because of the cross product Field from a Current Biot Savart Law G G We can immediately switch over from discrete charges to currents by replacing q v with Ids G o I dsG x r dB 4 r 2 This is the Biot Savart formula and like the differential form of Coulomb s Law provides a generic method for calculating fields
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