The Physics
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Electric Potential

Summary

• Definition
• Electric potential is…
• a scalar field
• used to explain the origin of the electric field, which is a vector field
• The electric potential difference between two locations is the work required to move a test charge from one location to another divided by the magnitude of the test charge.  ΔV = W q
• The electric potential difference between two locations is the ratio of the change in electric potential energy of a test charge to the magnitude of the test charge.  ΔV = ΔUE q
• Relation of electric potential to electric field
• The electric field at a point is space is the gradient of the electric potential at that point.
calculus version non-calculus version
 E = −∇V
 E̅ = − ∆V d
• The electric potential of a point in space is the path integral of the electric field starting from a point infinitely far away.
calculus version non-calculus version
 r V = − ⌠⌡ E · dr ∞
 ∆V = −E̅d
• Units
• The SI unit of electric potential is the volt.  ⎡⎣ V = J ⎤⎦ C
• The electric field has two frequently used, interchangeable SI units — the newton per coulomb and the volt per meter.  ⎡⎣ N = V ⎤⎦ C m
• The electron volt is an acceptable non SI unit of work and energy. It is used for some applications in electromagnetism; solid state, atomic, nuclear, and particle physics; and related sciences like biophysics, chemistry, and astronomy. An electronvolt is the work done a particle with one elementary charge when it is moved between two points with a potential difference of one volt.

1 eV = (1.6 × 10−16 C)(1 V) = 1.6 × 10−16 J