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The Coupling Constant

We are now ready to define our electrical "coupling constant" k_E. Referring to Eq.(15) we have

$$\phi \; [V] \; = \; k_E \, {Q \; [C] \over r \; [m]}$$

which we can rearrange to read

$$k_E \; = \; {\phi \; [V] \; \cdot \; r \; [m] \over Q \; [C]}$$

Thus k_E must have dimensions of {electric potential times distance per unit charge}; we can pick units of V-m/C to stick with convention. This still doesn't tell us the value of k_E. This must be measured. The result is

$$k_E % \; = \; 8.98755\cdots \times 10^9 \; \hbox{\rm V-m/C}$$ (17.19)