Potential energy of an electric dipole

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The discussion revolves around solving a textbook problem related to the potential energy of an electric dipole in a complex configuration. The main confusion lies in determining which electric fields to apply and how to analyze the dipole's position relative to other dipoles. A suggested approach is to initially place the central dipole and leave the other two at infinity, then gradually bring them closer to observe the resulting electric field direction. The participants are encouraged to evaluate which configuration requires less energy. The conversation emphasizes understanding the electric field's influence on the dipole's potential energy.
Samanko
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Homework Statement
When three electric dipoles are near each other, they each experience the electric field of the other two, and the three-dipole system has a certain potential energy. Figure shows two arrangenents in which three electric dipoles are side by side. Each dipole has the same magnitude of electric dipole moment, and the spacings between adjacent dipoles are identical. In which arrangrment is the potential energy of the three-dipole system greater?
Relevant Equations
U = - p • E
This is a problem from a textbook, and I can't solve it.
I know that the equation of Potential energy of electric dipole. Since the configuration is a little bit complicated. I'm confused applying which electric fields.
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Samanko said:
I'm confused applying which electric fields
Try the following: place the center dipole in its position, leave the other two at infinity (e.g. to left and right). Now bring those two closer until you have the final configuration. Which way does ##\vec E## point ? So which of (a) and (b) is easier (cheaper, lower energy) ?
 
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BvU said:
Try the following: place the center dipole in its position, leave the other two at infinity (e.g. to left and right). Now bring those two closer until you have the final configuration. Which way does ##\vec E## point ? So which of (a) and (b) is easier (cheaper, lower energy) ?
Thank you!
 
The book claims the answer is that all the magnitudes are the same because "the gravitational force on the penguin is the same". I'm having trouble understanding this. I thought the buoyant force was equal to the weight of the fluid displaced. Weight depends on mass which depends on density. Therefore, due to the differing densities the buoyant force will be different in each case? Is this incorrect?

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