As the plot of the story ( The Crucible) unfolds over time and Elizabeth finds out that her husband ( John Procter) has been having an affair with her maid ( Abigail Williams), she ( Elizabeth) becomes cold, detached and an emotionless women.
And after John took Elizabeth's side during certain argument and stood up for his wife, the Abigail could not that it anymore as she was still attached to John. Hence she decided to accuse Elizabeth of witchcraft to get her arrested and pull her out of the picture.
Hence, for the starting she ( Abigail) witnessed and encouraged Mary Warren's for making the poppet during court. After that Abigail instructed Mary to leave the needle into the poppet and took the poppet to the Elizabeth. This happened because Abigail has seen Mary sewing the poppet in the court and she already knew or guessed that Mary will give the doll to Elizabeth later.
to learn more about Witchcraft here
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