Lecture 16 Ch29 - PH 222-3A Spring 2007 Magnetic Fields Due...

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PH 222-3A Spring 2007 agnetic ields Due to Currents Magnetic Fields Due to Currents Lecture 16 Chapter 29 (Halliday/Resnick/Walker, Fundamentals of Physics 8 th edition) 1
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Chapter 29 agnetic Fields Due to Currents Magnetic Fields Due to Currents In this chapter we will explore the relationship between an electric current and the magnetic field it generates in the space around it. We will follow a two-pronged approach, depending on the symmetry of the roblem problem. For problems with low symmetry we will use the law of Biot-Savart in mbination with the principle of superposition. combination with the principle of superposition. For problems with high symmetry we will introduce Ampere’s law . oth approaches will be used to explore the magnetic field generated by Both approaches will be used to explore the magnetic field generated by currents in a variety of geometries (straight wire, wire loop, solenoid coil, toroid coil).We will also determine the force between two parallel, current-carrying conductors. We will then use this force to define the SI unit for electric current (the ampere). 2
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This law gives the magnetic field generated by a wire dB The Law of Biot -Savart G 0 3 4 i ds r dB r μ π × = GG G segment of length that carries a current . Consider the geometry shown in the figure. Associated with the element ds i ds we define an associated vector that has ds G A magnitude equal to the length . The direction of is the same as that of the current that flows through ds ds G segment . ds The magnetic field generated at point by the element located at point dB P ds A G G 0 3 is given by the equation . Here is the vector that connects 4 oint (location of element ) wit i ds r dB r r d s × = G G G G point atwhichwewanttodetermine . d B G point (location of element Ad 76 0 0 h point at which we want to determine The constant 4 10 T m/A 1.26 10 T m/A and is known as the sin "" The magnitude of is . Pd i ds B dB μπ θ −− = × G ermeability constant. 2 is 4 Here is the angle dB r permeability constant. between and . ds r 3
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Magnetic Field Generated by a Long Straight Wire The magnitude of the magnetic field generated by the wire at point cated at a distance from the wire P 0 located at a distance from the wire is given by the equation . i R μ 0 i 2 R B π 2 B R = The magnetic field lines form circles that have their centers at the wire. The magnetic field vector is tangent to the magnetic field lines. The sense for is given by the We p B B right - and rule G G int the thumb of the right hand in the . hand rule oint the thumb of the right hand in the direction of the current. The direction along which the fingers of the right hand curl around the wire gives the direction of . B G 4
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Proof of the equation.
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Lecture 16 Ch29 - PH 222-3A Spring 2007 Magnetic Fields Due...

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