What was the author's purpose for writing Act 2 of "The Crucible"?
There are many important things that happen in Act Two.
1. It gives us a glimpse at the fragile state that Elizabeth and John's relationship is in. We see right off the bat that they are awkward with one another, and tensions are right under the surface. As soon as Abby is brought up, John blows up and Elizabeth reveals her insecurities. We see that John's actions have had an impact on their family.
2. Mary Warren reveals, secondhand, what has been going on in the courts for the past while. Miller takes it from Abby and the girls calling out names at the end of Act One, to Mary Warren saying that "there be thirty-nine" arrested, and that "Goody Osburn-will hang!" We see just how much the accusations have gotten out of control.
3. Elizabeth is arrested: "Abigail Williams charge her" with witchcraft. This is crucial to the tension in the play, because her arrest is the catalyst that sends John to the courts for all of the action that happens in Act Three, including his revelation of his affair with Abby.
All of these events are crucial in increasing the tension, moving the story along, and revealing pertinent information about the characters and main action.
One of the main purposes for Act 2 is that it reveals the relationship of John and Elizabeth Proctor at this point in the play. In the beginning of the act the audience can tell that the relationship between the two is distant and strained -- Elizabeth seems very cold and unloving toward John while John tries his hardest to make Elizabeth happy and seeks her forgiveness. The two get angry with each other very easily and raise their voices because of this strained relationship.
A second purpose for this scene is to reveal the accusation of three major characters -- Rebecca Nurse, Martha Corey, and, most importantly, Elizabeth Proctor.
Finally, one of the themes of the play -- greed and jealousy -- are easily seen in the evident accusation of Elizabeth Proctor by Abigail through the use of a poppet and a needle that Abigail used to stab herself.