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Class 12 Tuition > Learn Additional Exercise 2 > Figure 2.34 shows a charge array known as an electric...
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Figure 2.34 shows a charge array known as an electric quadrupole. For a point on the axis of the quadrupole, obtain the dependence of potential on r for r/a >> 1, and contrast your results with that due to an electric dipole, and an electric monopole (i.e., a single charge).

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Four charges of same magnitude are placed at points X, Y, Y, and Z respectively, as shown in the following figure. A point is located at P, which is r distance away from point Y. The system of charges forms an electric quadrupole. It can be considered that the system of the electric quadrupole has three...
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Four charges of same magnitude are placed at points X, Y, Y, and Z respectively, as shown in the following figure. A point is located at P, which is r distance away from point Y. The system of charges forms an electric quadrupole. It can be considered that the system of the electric quadrupole has three charges. Charge +q placed at point X Charge −2q placed at point Y Charge +q placed at point Z XY = YZ = a YP = r PX = r + a PZ = r − a Electrostatic potential caused by the system of three charges at point P is given by, Since, is taken as negligible. It can be inferred that potential, However, it is known that for a dipole, And, for a monopole, read less
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