Ch0215

# Ch0215 - Chapter 15 Magnetic Field Intro Effects 15...

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Chapter 15 Magnetic Field Intro: Effects 115 15 Magnetic Field Intro: Effects We now begin our study of magnetism, and, analogous to the way in which we began our study of electricity, we start by discussing the effect of a given magnetic field without first explaining how such a magnetic field might be caused to exist. We delve into the causes of magnetic fields in subsequent chapters. A magnetic field is a vector field. That is, it is an infinite set of vectors, one at each point in the region of space where the magnetic field exists. We use the expression “magnetic field” to designate both the infinite set of vectors, and, when one is talking about the magnetic field at a point in space, the one magnetic field vector at that point in space. We use the symbol B harpoonrightnosp to represent the magnetic field. The most basic effect of a magnetic field is to exert a torque on an object that has a property known as magnetic dipole moment , and, that finds itself in the magnetic field. A particle or object that has a non-zero value of magnetic dipole moment is called a magnetic dipole. A magnetic dipole is a bar magnet. The value of the magnitude of the magnetic dipole moment of an object is a measure of how strong a bar magnet it is. A magnetic dipole has two ends, known as poles—a north pole and a south pole. Magnetic dipole moment is a property of matter which has direction. We can define the direction, of the magnetic dipole moment of an object, by considering the object to be an arrow whose north pole is the arrowhead and whose south pole is the tail. The direction in which the arrow is pointing is the direction of the magnetic dipole moment of the object. The unit of magnetic dipole moment is the A m 2 (ampere meter-squared) 1 . While magnetic compass needles come in a variety of magnetic dipole moments, a representative value for the magnetic dipole moment of a compass needle is . 1 A m 2 . Again, the most basic effect of a magnetic field is to exert a torque on a magnetic dipole that finds itself in the magnetic field. The magnetic field vector, at a given point in space, is the maximum possible torque-per-magnetic-dipole-moment-of-would-be-victim that the magnetic field would/will exert on any magnetic dipole (victim) that might find itself at the point in question. I have to say “maximum possible” because the torque exerted on the magnetic dipole depends not only on the magnitude of the magnetic field at the point in space and the magnitude of the magnetic dipole moment of the victim, but it also depends on the orientation of the magnetic dipole relative to the direction of the magnetic field vector. In fact: B μ τ harpoonrightnosp harpoonrightnosp harpoonrightnosp × = (15-1) where: τ harpoonrightnosp is the torque exerted on the magnetic dipole (the bar magnet) by the magnetic field, μ harpoonrightnosp is the magnetic dipole moment of the magnetic dipole (the bar magnet, the victim), and B harpoonrightnosp is the magnetic field vector at the location in space at which the magnetic dipole is.

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