The name is absent

V        2

∆V = ∫ dV = ∫ E ∙ dl

^V1          ¹

——

The link between the electric intensity E and the gradient of the voltage V V is:

——

E=-VV

where the gradient is a vector operator denoted V called Del or nabia (Morse &
Feshbach, 1953; Arfken, 1985; Kaplan, 1991; Schey, 1997).

(9)                  Vf ≡ grad(f )

The gradient vector is pointing towards the higher values of V, with magnitude
equal to the rate of change of values. The direction of Vf is the orientation in
which the directional derivative has the largest value and |Vf | is the value of
that directional derivative. The directional derivative V_uf (x₀, y₀, z₀) is the rate at
which the function f(x,y,z) changes at a point (x₀,y₀,z₀) in the direction u

(10)               V_uf ≡ VfU = lim ^f (x ⁺ h^u)^{- f} (^x)

^u         ∣u∣   h →o          h

and U is a unit vector Weisstein (2003).

Another vector not directly measurable that describes the electric field is the
vector of the electric induction D , which for isotropic dielectric is defined as:
(11)
where ε is the electric permittivity of the dielectric. The electric permittivity of the
vacuum is denoted with ε₀ ≈ 8.84 × 10^-12 F/m.

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