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I’d like to know if any constelation of 4 charges is a quadrupole. I have a task where there are 2 positive and 2 negative charged particles in the corners of a rectangle. And this is a quadrupole. Is it still one if I place them differently or if I have 3 positive and 1 negative? About the second question: I’d guess that it’s not a quadrupole anymore but a more complicated dipole.

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Yes, at some point in space their fields will sum to zero, for four charges this can happen in two locations. For example, if you have the charges evenly spaced in a plane ordered as (+,-,+,-) then you will have two quadrupoles midway between the charges at heights above the plane $\pm z_0$. If you have them ordered as (+,+,-,-) then the quadrupoles will be in the plane between the (+,+) section and (-,-) section.

It gets hard to imagine the field in your other scenario, I can imagine one scenario where the positive charges are on one side and the negative on the other. This configuration will give you two quadrupoles and a dipole. I'm not sure if this is the case generally.

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  • $\begingroup$ i dont exaclty know what you mean by this notation: (+,-,+,-) or (+,+). could you explain that ? $\endgroup$ – peter mafai May 30 at 18:54
  • $\begingroup$ + is a positive charge, - is a negative charge. The order in the brackets corresponds to the position in the plane. $\endgroup$ – jamie1989 May 30 at 18:56
  • $\begingroup$ okay. and you said they are evenly spaced. does that mean that they all have the same distance from each other ? so that they are placed on a cirlce $\endgroup$ – peter mafai May 30 at 19:10
  • $\begingroup$ @petermafai the charges can be placed along a line, a circle is not necessary. They also don't have to be evenly spaced, it's just the easiest scenario if you want to calculate that particular configuration. $\endgroup$ – jamie1989 May 30 at 19:13
  • $\begingroup$ @petermafai I can try and elaborate further if it still isn't clear? $\endgroup$ – jamie1989 May 31 at 8:30

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