In a region of space far from the charges that cause it, the electrostatic potential is $\displaystyle V(x, y, z) = \alpha\left(x^2 - y^2\right), \qquad \alpha = 250\ \text{V/m}^2$ with $x$, $y$ and $z$ in metres, measured from a point on a central axis, with $z$ along that axis. The potential does not depend on $z$. The charges that cause it all lie outside the region. Such a field is found near the middle of four long rods with charges $+, -, +, -$ in turn, as used to steer beams of ions. Which of the following statements are correct?