An electron of mass \(m\) and charge \(-e\) is projected with speed \(v_0\) at an angle \(\theta\) relative to the normal toward a large, uniformly charged nonconducting plate with negative surface charge density \(-\sigma\), where \(\sigma > 0\). The perpendicular stopping distance \(d\) is defined as the distance the electron travels toward the plate before the component of its velocity perpendicular to the plate momentarily becomes zero. Which of the following expressions correctly gives the stopping distance \(d\), and which statement correctly describes its limiting behavior as the launch angle \(\theta\) approaches \(\dfrac{\pi}{2}\)?