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Electric quadrupole. Figure 22-46 shows a generic electric
Chapter , Problem 21(choose chapter or problem)
Electric quadrupole. Figure 22-46 shows a generic electric quadrupole. It consists of two dipoles with dipole moments that are equal in magnitude but opposite in direction. Show that the value of E on the axis of the quadrupole for a point P a distance z from its center (assume z d) is given by in which Q (! 2qd2 ) is known as the quadrupole moment of the charge distribution
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QUESTION:
Electric quadrupole. Figure 22-46 shows a generic electric quadrupole. It consists of two dipoles with dipole moments that are equal in magnitude but opposite in direction. Show that the value of E on the axis of the quadrupole for a point P a distance z from its center (assume z d) is given by in which Q (! 2qd2 ) is known as the quadrupole moment of the charge distribution
ANSWER:E(z) = 2Q/z³
To show this, we write out the electric field of the two dipoles separately, then add them to get the total electric field of the quadrupole. The electric field of the first dipol