{"id":259716,"date":"2026-07-13T17:10:17","date_gmt":"2026-07-13T14:10:17","guid":{"rendered":"https:\/\/1kitap1.com\/en\/electromagnetics-for-engineers-fawwaz-ulaby-1\/"},"modified":"2026-07-13T17:10:17","modified_gmt":"2026-07-13T14:10:17","slug":"electromagnetics-for-engineers-fawwaz-ulaby-1","status":"publish","type":"post","link":"https:\/\/1kitap1.com\/en\/electromagnetics-for-engineers-fawwaz-ulaby-1\/","title":{"rendered":"Electromagnetics For Engineers – Fawwaz Ulaby (1)"},"content":{"rendered":"
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(6.5) Understationaryconditions,thed-ccurrentinthecoilpro- duces a constant magnetic \ufb01eld B, which in turn produces aconstant\ufb02uxthroughtheloop.Whenthe\ufb02uxisconstant, nocurrentisdetectedbythegalvanometer.However,when thebatteryisdisconnected,therebyinterruptingthe\ufb02owof currentinthecoil,themagnetic\ufb01elddropstozero,andthe consequent change in magnetic \ufb02ux causes a momentary de\ufb02ection of the galvanometer needle. When the battery isreconnected,thegalvanometeragainexhibitsamomen- taryde\ufb02ection,butintheoppositedirection.Thus,current isinducedintheloopwhenthemagnetic\ufb02uxchanges,and the direction of the current depends on whether the \ufb02ux is increasing (as when the battery is being connected) or decreasing (as when the battery is being disconnected). It was further discovered that current can also \ufb02ow in the loop,whilethebatteryisconnectedtothecoil,iftheloopis turnedaroundsuddenlyorwhilemovingitclosertooraway from the coil.<\/p>\n

The physical movement of the loop changes the amount of \ufb02ux linking its surface S, even though the \ufb01eld B due to the coil has not changed. A galvanometer is the predecessor of the voltmeter and ammeter.Whenagalvanometerdetectsthe\ufb02owofcurrent through the coil, it means that a voltage has been induced across the galvanometer terminals. This voltage is called the electromotive force (emf), Vemf, and the process is called electromagnetic induction. The emf induced in a closed conducting loop of N turns is given by Vemf = \u2212N d\u0010 dt = \u2212N d dt B \u00b7 ds (6.6) Even though the results leading to Eq.<\/p>\n

(6.6) were also dis- covered independently by Henry, Eq. (6.6) is attributed to Faraday and is known as Faraday\u2019s law. The signi\ufb01cance of the negative sign in Eq. (6.6) will be explained in the next section. We note that the derivative in Eq. (6.6) is a total time derivative that operates on the magnetic \ufb01eld B, as well as the differential surface area ds.<\/p>\n

Accordingly, an emf can be generated in a closed conducting loop under any of the following three conditions: 1. A time-varying magnetic \ufb01eld linking a stationary loop; the induced emf is then called the transformer emf, V tr emf. 2. A moving loop with a time-varying area (relative to the normal component of B) in a static \ufb01eld B; the induced emf is then called the motional emf, V m emf. 3.<\/p>\n

A moving loop in a time-varying \ufb01eld B. The total emf is given by Vemf = V tr emf + V m emf, (6.7) with V m emf = 0 if the loop is stationary (case (1)) and V tr emf = 0 if B is static (case (2)). For case (3), neither term is zero. Each of the three cases will be examined separately in the following sections. 6-2 Stationary Loop in a Time-Varying Magnetic Field The single-turn, conducting, circular loop with con- tour C and surface area S shown in Fig.<\/p>\n

6-2(a) is in a time-varying magnetic \ufb01eld B(t). As was stated earlier, the emf induced when S is stationary and the \ufb01eld is time varying is called the transformer emf and is denoted V tr emf. Since the loop is stationary, d\/dt in Eq. (6.6) now operates on B(t) only.<\/p>\n

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The University of Michigan Ann Arbor, MI 48109 Copyright \uf8e9 2025 Fawwaz T. Ulaby This book is published by Michigan Publishing under an agreement with the authors. It is made available free of charge in electronic form to any student or instructor interested in the subject matter. Published in the United States of America by Michigan Publishing. Manufactured in the United States of America ISBN 978-1-60785-911-6 (hardcover) ISBN 978-1-60785-912-3 (electronic) The free ECE Textbook initiative is sponsored by the ECE Department at the University of Michigan.<\/p>\n<\/blockquote>\n

This is a short excerpt from the opening of “” by Unknown, quoted for review and introduction purposes. All rights belong to the copyright holders.<\/em><\/p>\n

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