= Solution
In uniform fields, a rigid neutral <electric dipole> with both charges moving at the selected common velocity has zero net translational force. To leading nonrelativistic order its torque is $\boldsymbol\tau=\mathbf p\times(\mathbf E+\mathbf v\times\mathbf B)$, which also vanishes at the velocity-selector condition. Thus it continues undeflected and, initially nonrotating, does not start rotating in the ideal balanced fields. An unbalanced effective field could exert a torque; the dipole orientation is not otherwise specified.
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