Solution:
The potential energy (\(U\)) of an electric dipole in a uniform electric field is given by:
\[
U = -\mathbf{p} \cdot \mathbf{E} = -pE \cos\theta
\]
Here:
- \(p\) is the magnitude of the dipole moment,
- \(E\) is the magnitude of the electric field,
- \(\theta\) is the angle between \(\mathbf{p}\) and \(\mathbf{E}\).
The potential energy is largest when \(-\cos\theta\) is most positive, i.e., when \(\cos\theta = -1\). This happens at:
\[
\theta = \pi \ (\text{180°})
\]
At this angle, the dipole is aligned opposite to the electric field, and the potential energy is \(U = +pE\), its maximum value.
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