tailieunhanh - Fundamentals of Engineering Electromagnetics - Chapter 3

Trong sơ đồ này, C1 và C2 chỉ các điện dung với mặt đất của dây dẫn và thăm dò, tương ứng, và CM đại diện cho điện dung lẫn nhau của họ. Q1 phí trên dây dẫn sẽ được đưa ra bởi [44] Q1 Â ¼ C1 V1 Ã ¾ CM Ã ° V1 Ã € V2 AZ Ã ° 2:51 AZ Các vòng lặp phản hồi của đồng hồ sẽ nâng cao khả năng của tàu thăm dò cho đến khi V2 Â ¼ V1, để Eq. (2,51) trở thành V1 Â ¼ Q1 C1 Ã ° 2:52 AZ | Applied Electrostatics 79 In this diagram C1 and C2 denote the capacitances to ground of the conductor and probe respectively and CM represents their mutual capacitance. The charge 21 on the conductor will be given by 44 21 C1V1 Cm V1 - V2 The feedback loop of the meter will raise the potential of the probe until V2 V1 so that Eq. becomes V1 21 C1 This unambiguous result reflects the potential of the floating conductor with the probe absent. One of the more common uses of noncontacting voltmeters involves the measurement of charge on insulating surfaces. If surface charge on an insulating layer is tightly coupled to an underlying ground plane as in Fig. the surface potential Vs of the charge layer will be well defined. Specifically if the layer has thickness d the surface potential becomes Vs E d The surface charge and its ground-plane image function as a double layer that introduces a potential jump between the ground plane and the upper surface of the insulator. The potential of a noncontacting voltmeter probe placed near the surface will be raised to the same potential Vs allowing the surface charge ps to be determined from Eq. . If the charge on the insulator is not tightly coupled to a dominant ground plane its surface potential will be strongly influenced by the position of the probe as well as by the insulator s position relative to other conductors and dielectrics. Under these conditions the reading of the noncontacting voltmeter becomes extremely sensitive to probe position and cannot be determined without a detailed analysis of the fields surrounding the charge 45 . Such an analysis must account for two superimposed components the field Eq produced by the measured charge with the probe grounded and the field EV created by the voltage of the probe with the surface charge absent. The voltmeter will raise the probe potential until a null-field condition with Eq EV 0 is reached. Determining the relationship between the resulting