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# Electric Potential

## Summary

• Definition
• The 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.  ∆V = 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.  ∆V = ∆UE 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
 E = − ∆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 = −Ed
• Units
• The SI unit of electric potential is the volt.  ⎡⎢⎣ V = J ⎤⎥⎦ C
• The electric field has two frequently used, equivalent SI units…
• the newton per coulomb and
• the volt per meter.
 ⎡⎢⎣ N = V ⎤⎥⎦ C m
• The electronvolt 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 (1 eV) is the work done on a particle with one elementary charge (1 e) when it is moved between two locations with a potential difference of one volt (1 V).

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