Multimediální učebnice

Slovník pojmů

Scalar potential

Scalar potential simplifies the investigation of the influence of static charges (time derivative equals to zero). Field is then described by the first and the third Maxwell equation in the form

rot E = 0

div E = 0

( 1 )

Since curl of gradient identically equals to zero, (1) is met if

E = - grad φ

( 2 )

(j is scalar potential). Hence, the single scalar equation (Laplace one) has to be solved

\nabla^{2} φ = 0

( 3 )

Eqn. (3) is valid in every region, where potential is finite and continuous. Thanks to (3), the field is described by a single partial differential equation for a scalar function j.

Physical notion j can be built on the basis of (2)

E \cdot d r = - grad φ \cdot d r = - d φ

Since the product E .d r equals to the work, which is performed by the field when moving unitary charge along the elementary path dr, elementary potential dj equals to the decrease (therefore minus) of the potential energy of this unitary charge in electrostatic field.

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