The relationship between "enchant" and "captivate" is that these two words are synonyms. So, we are looking for a word that is a synonym of "urge."
Step 1: Analyzing the options.
- (A) "confuse" is not a synonym of "urge," so it doesn’t fit the analogy.
- (B) "avert" means to prevent or avoid, and is not a synonym of "urge."
- (C) "disagree" is not a synonym of "urge," as it refers to differing opinions.
- (D) "enforce" means to compel obedience, which is not synonymous with "urge."
- (E) "encourage" is a synonym of "urge" because both mean to prompt or stimulate action.
Step 2: Conclusion.
The correct analogy is \( \boxed{(E)} \), where "urge" is to "encourage" as "enchant" is to "captivate."