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