In Harper Lee's To Kill a Mockingbird, conflict between Bob Ewell and Atticus arises when Ewell and his daughter take the witness stand in the courtroom in chapters 17 and 18.
Conflict first arises when Atticus has Ewell write his name before the court to prove he is left-handed. The point of proving he is left-handed is to show that Ewell could have easily been the one to abuse his daughter Mayella since her right eye was blackened, which could have only been done if someone facing her hit her with a left hand. Ewell may be very uneducated and dumb, but he's not dumb enough to miss Atticus's implications, as he shows when he, as Scout narrates, complains that "tricking lawyers like Atticus Finch took advantage of him all the time with their tricking ways."
The conflict continues to develop when Mayella takes the witness stand. Through questioning, Atticus is able to get Mayella to confess that her father is not abusive, "except when he's drinking." Her testimony, through Atticus's questioning, further calls into question the fact that she has seven younger siblings when her mother has been dead longer than she can remember. It is also during Mayella's testimony that Atticus has Tom Robinson stand to reveal that his left arm and hand are shriveled and crippled from having been caught in a cotton gin. Hence, it is through Mayella's testimony that Atticus proves it would have been impossible for Robinson to have bruised Mayella on the right side of her face while facing her but very possible for her father to have done so. Both Ewell and Mayella are very aware of the fact that Atticus has called into question the truth of their testimony as well as the honorableness of Ewell's character, and this awareness creates conflict between Atticus and Ewell.