volt per metre

SI coherent derived unit whose name and symbol includes an SI coherent derived unit with a special name and symbol

Name	Symbol	Quantity	Base units
volt per metre	V/m	electric field strength	kg m s⁻³ A⁻¹
The volt per metre, symbol V/m, is the SI coherent derived unit of electric field strength. One volt per metre is equal to the strength of the electric field produced when a potential difference of one volt is applied between two parallel conducting plates spaced one metre apart.
Definition			h c^-1 Δν_Cs² e^-1
$1 \mspace{4mu} \text{V} / \text{m} \mspace{6mu} = \dfrac{(299 \mspace{4mu} 792 \mspace{4mu} 458)(1.602 \mspace{4mu} 176 \mspace{4mu} 634 \times 10^{-19})}{(6.626 \mspace{4mu} 070 \mspace{4mu} 15 \times 10^{-34})(9 \mspace{4mu} 192 \mspace{4mu} 631 \mspace{4mu} 770)^2} \mspace{6mu} \dfrac{h \mspace{4mu} {\Delta \nu _{Cs}}^2}{c \mspace{4mu} e}\\ \\ \\ 1 \mspace{4mu} \text{V} / \text{m} \mspace{6mu} \approx 8.578 \mspace{4mu} 183 \mspace{4mu} 642 \mspace{4mu} 944 \mspace{4mu} 178 \mspace{4mu} 366 \times10^{2} \mspace{6mu} h \mspace{4mu} c^{-1} \mspace{4mu} {\Delta \nu _{Cs}}^2 \mspace{4mu} e^{-1}$

Electric fields

An electrically charged particle, Q, present in an electric field, E, experiences a force, F, directly proportional to the strength of the electric field and the magnitude of the charge.

$F \propto \mathbf{E} \mspace{2mu} {Q}$

Using SI coherent units,

$F = \mathbf{E} \mspace{2mu} {Q}\\ \\ \\ \mathbf{E} = \dfrac{F}{Q}$

where:

E is the strength of the electric field in volts per metre, symbol V m^-1,
F is the force exerted on the particle in newtons, symbol N,
Q is the electric charge of the particle in coulombs, symbol C.

A force of one newton is exerted on a particle with a charge of one coulomb in an electric field of one volt per metre.

$1 \mspace{4mu} \text{N} \mspace{4mu} = \mspace{4mu} 1 \mspace{4mu} \text{V} \mspace{4mu} \text{m}^{-1} \mspace{4mu} \times \mspace{4mu} 1 \mspace{4mu} \text{C}$

Thus, one volt per metre, symbol V m^-1, is equivalent to one newton per coulomb, symbol N C^-1.

$1 \mspace{4mu} \text{V} \mspace{4mu} \text{m}^{-1} \mspace{4mu} = \mspace{4mu} \dfrac{1 \mspace{4mu} \text{N}}{1 \mspace{4mu} \text{C}}$