tailieunhanh - Electromagnetic Field Theory: A Problem Solving Approach Part 43

Electromagnetic Field Theory: A Problem Solving Approach Part 43. Electromagnetic field theory is often the least popular course in the electrical engineering curriculum. Heavy reliance on vector and integral calculus can obscure physical phenomena so that the student becomes bogged down in the mathematics and loses sight of the applications. This book instills problem solving confidence by teaching through the use of a large number of worked problems. To keep the subject exciting, many of these problems are based on physical processes, devices, and models. This text is an introductory treatment on the junior level for a two-semester electrical engineering. | Faraday s Law of Induction 395 When the switch was later opened another transient current flowed in loop 2 this time in the same direction as the original current in loop 1. Currents are induced in loop 2 whenever a time varying magnetic flux due to loop 1 passes through it. In general a time varying magnetic flux can pass through a circuit due to its own or nearby time varying current or by the motion of the circuit through a magnetic Held. For any loop as in Figure 6-2 Faraday s law is f d f EMF 6 E-dl - - B dS 4 di dt Js 1 where EMF is the electromotive force defined as the line integral of the electric field. The minus sign is introduced on the right-hand side of 1 as we take the convention that positive flux flows in the direction perpendicular to the direction of the contour by the right-hand rule. 6-1-2 Lenz s Law The direction of induced currents is always such as to oppose any changes in the magnetic flux already present. Thus in Faraday s experiment illustrated in Figure 6-1 when the switch in loop 1 is first closed there is no magnetic flux in loop 2 so that the induced current flows in the opposite direction with its self-magnetic field opposite to the imposed field. The induced current tries to keep a zero flux through A B dS s i E dl - B dS L at s Figure 6-2 Faraday s law states that the line integral of the electric field around a closed loop equals the time rate of change of magnetic flux through the loop. The positive convention for flux is determined by the right-hand rule of curling the fingers on the right hand in the direction of traversal around the loop. The thumb then points in the direction of positive magnetic flux. 396 Electromagnetic Induction loop 2. If the loop is perfectly conducting the induced current flows as long as current flows in loop 1 with zero net flux through the loop. However in a real loop resistive losses cause the current to exponentially decay with an L R time constant where L is the self-inductance of the loop and R .

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