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I) The Dirac delta distribution (and derivative thereof) in the dipole field $$\Phi ~=~\frac{1}{4\pi\varepsilon}\frac{\vec{p}\cdot \vec{r}}{r^3} \tag{1}$$ $$\Downarrow$$ $$\vec{E}~=~-\vec{\nabla}\Phi ~=~ \frac{1}{4\pi\varepsilon}\frac{3(\vec{p}\cdot \vec{r})\vec{r}-r^2\vec{p} }{r^5} -\frac{\vec{p}}{3\varepsilon}\delta^3(\vec{r}) \tag{2}$$ $$\Downarrow$$ ...

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The mass of a ball is scalar. Its potential energy is stored in its position in a gravitation field. A dipole has its potential energy in its orientation with regards to an external field. It can do work by exerting torque when orienting along the field.

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I want to find out the potential energy of a electric dipole in a uniform electric field by another process which gives the result to $U= -P.E$. Purpose A, B are the position of the point charges $q$ and $-q$ and seperated by small distance D and O be the position of the origin. The distance from O to $-q$ is R. So potential energy, $U=-q.v(R) q.v(R D)$ ...

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Consider two atoms at some distance $R$ from each other. The Hamiltonian of this system is then the sum of the Hamiltonians of the two atoms plus interaction terms involving the electrostatic interaction between the electrons of one atom with the electron and nucleus of the other atom. You can then calculate what the shift in the ground state energy of the ...

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You may be confusing torque and force. The force $\vec{\mathrm{F}}$ is given by $q\, \vec{\mathrm{E}}$, so you can clearly see that the force is in different directions for the positive and negative charges, and is either parallel or antiparallel to the electric field. The torque $\vec{\tau}$ about any point $O$ is given by \$\vec{\mathrm{r}} \times ...

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