  We study the effect of the Born-Infeld electric field on the supersymmetric
configuration of various composite D-branes. We show that the generic values of
the electric field do not affect the supersymmetry but, as it approaches
$1/2\pi\alpha'$ keeping the magnetic field finite, various combinations of the
magnetic fields allow up to 8 supersymmetries. We also explore the unbroken
supersymmetries for two intersecting D-strings which are in uniform or relative
motion. For a finite uniform Lorentz boost, 16 supersymmetries are guaranteed
only when they are parallel. For an infinite one, 8 supersymmetries are
preserved only when both the D-strings are oriented to the forward or backward
direction of the boost. Under a finite relative boost, 8 supersymmetries are
preserved only when the intersecting angle is less than $\pi/2$ and the
intersecting point moves at the speed of light. As for an infinite relative
boost, 8 supersymmetries are preserved regardless of the values of the
intersecting angle.
