Consider the following sentence.


Can I replace 存在 with ある as follows?


Bonus question: What does ~下に mean in 磁束が変動する環境下に ?


Yes, you could for the meaning, but it would not be advisable to do so because that would create some imbalance in the over-all formality of the sentence.

This sentence is very stiff and academic as it should be. If you replaced one of the words by another word with the same meaning but with a lower level of formality (存在する vs. ある, in this case), the result would almost always be less than ideal.

Finally, that 「下」 is read 「か」 and it is a suffix meaning "in", "under", etc.

「影響下{えいきょうか}」 = "under the influence (of)"

Other common examples:

「フランスの支配下{しはいか}にある国」= "a country under the control of France"

「インフレ下{か}の日本」= "Japan in recession"

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