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Regard as a volume of space in which the electric potential is 125,000 volts (at every point in the volume of space) and what is the electric field in that region of space?
Answer: In any region of space we are able to establish a Cartesian coordinate system. In expressions of the position variables x, y, z of that coordinate system the electric field components Ex, Ey, and Ez depend on the electric potential V as:
, and For the reason that V is a constant all three derivatives yield zero. This signifies that every component of the electric field is zero. If each component of the electric field is zero then the electric field is zero.
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