Undergrad What are the stable orientations for a dipole in an external e-field

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Stable orientations for a dipole in an external electric field occur when the dipole aligns with the field direction, minimizing potential energy. If the dipole is slightly perturbed from this alignment, it experiences a restoring torque that returns it to the stable position. The stability of these orientations depends on whether the external field is uniform; in a uniform field, the dipole will return to equilibrium, while in a non-uniform field, it may move toward regions of higher field strength. The discussion emphasizes the importance of understanding the dipole's behavior in varying field conditions. Overall, the dipole's orientation and response to perturbations are crucial for applications in electrostatics.
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What are the stable orientation(s) for a dipole in an external electric field? What happens if the dipole is slightly perturbed from these orientations?
 
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Is the external field uniform?
 
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