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Yes. Stationary electric (electrostatic) fields will act on each other and a force will be developed. If you had a standing electric field and could "beam in" an electron (a la Star Trek), the electron would react at once and move either toward a positive field source or away from a negative field source. The electron would know the field was there the instant it appeared.

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Q: If a stationary electron sat inside a stationary electric field would the electric field cause the electron to move?
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