Chapter 30 - 30 Sources of the Magnetic Field CHAPTER...

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30 CHAPTER OUTLINE 30.1 The Biot-Savart Law 30.2 The Magnetic Force Between Two Parallel Conductors 30.3 Ampère’s Law 30.4 The Magnetic Field of a Solenoid 30.5 Magnetic Flux 30.6 Gauss’s Law in Magnetism 30.7 Displacement Current and the General Form of Ampère’s Law 30.9 The Magnetic Field of the 30.8 Magnetism in Matter Earth Sources of the Magnetic Field ANSWERS TO QUESTIONS Q30.1 It is not. The magnetic field created by a single loop of current resembles that of a bar magnet—strongest inside the loop, and decreasing in strength as you move away from the loop. Neither is it in a uniform direction—the magnetic field lines loop though the loop! Q30.2 No magnetic field is created by a stationary charge, as the rate of flow is zero. A moving charge creates a magnetic field. Q30.3 The magnetic field created by wire 1 at the position of wire 2 is into the paper. Hence, the magnetic force on wire 2 is in direction down × into the paper = to the right, away from wire 1. Now wire 2 creates a magnetic field into the page at the location of wire 1, so wire 1 feels force up × into the paper = left, away from wire 2. FIG. Q30.3 185
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186 Sources of the Magnetic Field Q30.4 No total force, but a torque. Let wire one carry current in the y direction, toward the top of the page. Let wire two be a millimeter above the plane of the paper and carry current to the right, in the x direction. On the left-hand side of wire one, wire one creates magnetic field in the z direction, which exerts force in the ±± ± ik j ×= direction on wire two. On the right-hand side, wire one produces magnetic field in the ± k direction and makes a ±±± ik j ×− =+ ej force of equal magnitude act on wire two. If wire two is free to move, its center section will twist counterclockwise and then be attracted to wire one. 1 2 FIG. Q30.4 Q30.5 Ampère’s law is valid for all closed paths surrounding a conductor, but not always convenient. There are many paths along which the integral is cumbersome to calculate, although not impossible. Consider a circular path around but not coaxial with a long, straight current-carrying wire. Q30.6 The Biot-Savart law considers the contribution of each element of current in a conductor to determine the magnetic field, while for Ampère’s law, one need only know the current passing through a given surface. Given situations of high degrees of symmetry, Ampère’s law is more convenient to use, even though both laws are equally valid in all situations. Q30.7 If the radius of the toroid is very large compared to its cross-sectional area, then the field is nearly uniform. If not, as in many transformers, it is not. Q30.8 Both laws use the concept of flux—the “flow” of field lines through a surface to determine the field strength. They also both relate the integral of the field over a closed geometrical figure to a fundamental constant multiplied by the source of the appropriate field. The geometrical figure is a surface for Gauss’s law and a line for Ampère’s.
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This homework help was uploaded on 04/13/2008 for the course PHYS 211 taught by Professor Shannon during the Spring '08 term at MSU Bozeman.

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Chapter 30 - 30 Sources of the Magnetic Field CHAPTER...

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