Electric potential is the work done per unit positive charge in bringing it from infinity to a point: V = Q / (4πε₀r). It falls off as 1/r, more gently than the 1/r² field. The field is the negative gradient of the potential, E = −dV/dr, so the steeper the potential curve, the stronger the field.
MissionPredict how the potential of a point charge varies with distance.Streak 0Best 0
The electric potential of a point charge varies with distance as:
potential V = Q / (4πε₀r)—
field strength E = Q / (4πε₀r²)—
Blue is the potential (1/r), green is the field (1/r²). The field is the negative gradient of the potential: where V drops steeply, E is large.