Is the 'test charge' in electric potential energy defined as immobile?

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Hello, quick question, when EPE was defined, did we decide that the "test charge" is immobile in the field? Otherwise a force equal and opposite to that of the electric field would just stop the charge from accelerating.
 
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A test charge ##q## is just an artifact that can be considered as "an electric field measuring device". If you can measure the force vector ##\vec F## on it at a given point in space, then ##\vec F/q## gives the electric field at that point in space.