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1. From equation: in the equation of V(2), there are only diagonal terms in the matrix and V_xx and V_yy are the same.
2. Visually: in the picture of the toy model you can imagine the dumbell “spinning” around the z-axis without it changing the electric field gradient. The system is invariant under rotations of the x-y plane about the z-axis, thus there is axial symmetry.
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