The personal conflict between Jack and Ralph mirrors the theme of "the eternal battle between good and evil," with Jack representing evil and Ralph representing good. In the course of the novel, good is overcome by evil. The conflict and the eventual takeover of good by evil is represented in the novel by the situations in which Jack and Ralph begin to become frustrated with one another.
One example of the brewing conflict appears in chapter four, when Ralph and Jack quarrel over the fire. Jack has become obsessed with hunting and catching a pig. Jack had been left to care for the fire, something vital to the boys' survival and rescue, and Jack chose to abandon the fire to go hunting. When Ralph discovers that the fire has gone out, the two boys argue about priorities.
Then, in chapter five, Jack and Ralph have a public disagreement over which of the two has personified "the beast" of whom the little'uns have become terrified. Ralph tries to stress the importance of order, values, and the fire, while Jack makes a passionate speech about the beast and hunting. Jack is the one met with roaring applause. Jack and Ralph then become embroiled in a greater conflict about "rules," which Ralph declares, "is all we've got," while Jack screams, "Bullocks to the rules—we're strong, we'll hunt!"
I recommend for more examples continuing to look in chapter five, and also in chapters six and seven.