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How do we know that E1 and E2 have the same magnitude? Is that always the case, even though one is closer and one has a stronger charge than the other?

Hi magiemay480, thanks for your question. E1 and E2 having equal magnitude is a special case for this question. The reason for it is that the electric field at point "P" is zero, and the only way for that to be possible is if E1 and E2 are of equal magnitude in opposite directions.

Hope that helps,
Mr. Dychko

Thanks so much, Mr. Dychko! You were a lifesaver in my last course and are continuing to be invaluable in E&M as well! :)

You're welcome! I'm glad the videos are helping!