Electromagnetic Field Theory: A Problem Solving Approach Part 21. 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. | Capacitance 175 the electrodes is as if the end effects were very far away and not just near the electrode edges. We often use the phrase neglect fringing to mean that the nonuniform field effects near corners and edges are negligible. With the neglect of fringing field effects near the electrode ends the electric field is perpendicular to the electrodes and related to the voltage as Ex dx v Ex v l 1 The displacement vector is then proportional to the electric field terminating on each electrode with an equal magnitude but opposite polarity surface charge density given by Dx eEx Tf x 0 Tf x l ev l 2 The charge is positive where the voltage polarity is positive and vice versa with the electric field directed from the positive to negative electrode. The magnitude of total free charge on each electrode is qf rf x 0 A v 3 The capacitance C is defined as the magnitude of the ratio of total free charge on either electrode to the voltage difference between electrodes C v I permittivity electrode area r .24 -1 -2 ------------------ ------------farad A -s -kg -m 1 spacing 4 Even though the system remains neutral mobile electrons on the lower electrode are transported through the voltage source to the upper electrode in order to terminate the displacement field at the electrode surfaces thus keeping the fields zero inside the conductors. Note that no charge is transported through free space. The charge transport between electrodes is due to work by the voltage source and results in energy stored in the electric field. In SI units typical capacitance values are very small. If the electrodes have an area of A 1 cm2 10-4 m2 with spacing of I 1 mm CIO-3 m the free space capacitance is C x 10 farad. For this reason usual capacitance values are expressed in microfarads 1 xf 10 6 farad nanofarads 1 nf 10-9 farad and picofarads 1 pf 10-12 farad . 176 Polarization and Conduction With a linear dielectric of permittivity e as in Figure 3-18a the field of 1 remains unchanged for a .
