By Hermann A. Haus
Hardcover: 742 pages
Publisher: Prentice corridor (September 1989)
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Additional info for Electromagnetic Fields and Energy
Where λf , the total ﬂux of magnetic ﬁeld linking the coil, is deﬁned as the ﬂux linkage. Note that Faraday’s law makes it possible to measure µo H electrically (as now demonstrated). 1. Voltmeter Reading Induced by Magnetic Induction The rectangular coil shown in Fig. 4 is used to measure the magnetic ﬁeld intensity associated with current in a wire. 1. The height and length of the coil are h and l as shown, and because the coil has N turns, it links the ﬂux enclosed by one turn N times. 10), evaluation of (8) gives � z+l � R+h λf = µo N z R � i drdz = 2πr � µo N l h ln 1 + 2π R �� i (9) In the experiment, the current takes the form i = I sin ωt (10) 36 Maxwell’s Integral Laws in Free Space Chapter 1 where ω = 2π(60).
5 is negligible. So long as the ﬁeld probe is within a distance r from the wire that is small compared to the distance to the ends of the wire or to the return wires below, the magnetic ﬁeld intensity is predicted quantitatively by (10). The curve shown is typical of demonstration measurements illustrating the radial dependence. Because the Halleﬀect probe fundamentally exploits the Lorentz force law, it measures the ﬂux density µo H. A common unit for ﬂux density is the Gauss. For conversion of units, 10,000 gauss = 1 tesla, where the tesla is the SI unit.
6. As in the previous illustration, the line integral is the product of the circumference and Hφ . The surface integral gives nothing if r < R, but gives 2πR times the surface current density if r > R. Thus, � 2πrHφ = 0; 2πRKo ; r