= Solution
For the intended force-balanced straight-line motion, the <Lorentz force> vanishes:
$$
\boxed{\mathbf E+\mathbf v\times\mathbf B=0.}
$$
For a nonzero uniform <magnetic field>, this implies $\mathbf E\cdot\mathbf B=0$ and
$$
\mathbf v_\perp=\frac{\mathbf E\times\mathbf B}{B^2},
$$
while a component parallel to $\mathbf B$ is unrestricted. A straight trajectory by itself states only that the force has no transverse component, $\mathbf v\times(\mathbf E+\mathbf v\times\mathbf B)=0$. For example, parallel electric field and motion can give straight but accelerated motion. The boxed cancellation is the usual constant-velocity interpretation of the source.
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