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title: "A physical dipole consists of two point charges, \\(+q\\) and \\(-q\\), fixed at a distance \\(d\\) apart, giving a dipole moment of magnitude \\(p = qd\\). The dipole is centered at position \\(x = x_0\\) in a region with an electric field directed along the \\(x\\)-axis given by \\(E(x) = E_0 + bx\\), where \\(E_0\\) and \\(b\\) are positive constants. Initially, the dipole is oriented parallel to the field, with \\(+q\\) at \\(x = x_0 + \\dfrac{d}{2}\\) and \\(-q\\) at \\(x = x_0 – \\dfrac{d}{2}\\). The dipole is then rotated by \\(180^\\circ\\) about its center \\(x_0\\) so that it is oriented antiparallel to the field. What is the change in electric potential energy \\(\\Delta U\\) of the dipole system resulting from this rotation?"
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url: "https://nerd-notes.com/ubq/118125/"
date_modified: "2026-08-04T08:05:18+00:00"
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# A physical dipole consists of two point charges, \(+q\) and \(-q\), fixed at a distance \(d\) apart, giving a dipole moment of magnitude \(p = qd\). The dipole is centered at position \(x = x_0\) in a region with an electric field directed along the \(x\)-axis given by \(E(x) = E_0 + bx\), where \(E_0\) and \(b\) are positive constants. Initially, the dipole is oriented parallel to the field, with \(+q\) at \(x = x_0 + \dfrac{d}{2}\) and \(-q\) at \(x = x_0 – \dfrac{d}{2}\). The dipole is then rotated by \(180^\circ\) about its center \(x_0\) so that it is oriented antiparallel to the field. What is the change in electric potential energy \(\Delta U\) of the dipole system resulting from this rotation?

A physical dipole consists of two point charges, \(+q\) and \(-q\), fixed at a distance \(d\) apart, giving a dipole moment of magnitude \(p = qd\). The dipole is centered at position \(x = x_0\) in a region with an electric field directed along the \(x\)-axis given by \(E(x) = E_0 + bx\), where \(E_0\) and \(b\) are positive constants. Initially, the dipole is oriented parallel to the field, with \(+q\) at \(x = x_0 + \dfrac{d}{2}\) and \(-q\) at \(x = x_0 - \dfrac{d}{2}\). The dipole is then rotated by \(180^\circ\) about its center \(x_0\) so that it is oriented antiparallel to the field. What is the change in electric potential energy \(\Delta U\) of the dipole system resulting from this rotation?

- **A.** \(2p(E_0 + bx_0)\)
- **B.** \(2p(E_0 + bx_0) + pbd\)
- **C.** \(2pE_0 + pbd\)
- **D.** \(2pbx_0\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/118125/*