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Chapter 30 Sources of Magnetic Field

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Introduction This chapter will focus on the sources of magnetic fields: moving charges. Well look at the field created by a current carrying conductor, as well as other symmetrical current distributions. Well look at the force between two current- carrying conductors. Well finish by looking at the processes that result in materials being naturally magnetic.

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30.1 The Biot-Savart Law Shortly after Oersted discovers that a compass needle is deflected by a nearby current- carrying conductor (1819) Jean-Baptiste Biot and Felix Savart begin quantitative experimentation. Their experimental results have given a mathematical expression for the magnetic field at some point in space in terms of the current that causes it.

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30.1 We will summarize results of their experiment concerning the magnetic field dB at a point P associated with a length element ds on a wire carrying current I.

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30.1 The results: The vector dB is perpendicular to both ds and r. The magnitude of dB is inversely proportional to r 2, where r is the distance from ds to point P. The magnitude of dB is proportional to the current and to the magnitude of ds. The magnitude of dB is proportional to sin , where is the angle between ds and r.

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30.1 The mathematical expression summarizng these observations is known as the Biot-Savart Law: Remember o is the permeability of free space Again, note that dB is only the field created by a single element of the conductor and to find the total magnetic field B at point P, we must integrate.

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30.1 Integration gives We must be careful with this integration as in does involved the vector cross product. For direction of the B field, the right hand rule is used. Point thumb in direction of I, curling fingers show the direction of B.

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30.1 Quick Quiz p. 928 Example 30.1 Resulting Equations 30.2, 30.3

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30.2 Magnetic Force between Two Parallel Conductors If we have two current carrying wires, the B field caused by one current will exert a force on the other. If the conductors are parallel to each other, then the B field is perpendicular to the current.

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30.2 The force on wire one from B-Field two is And assuming long wires (