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  1. Coulombs Law

    Linked via "unit vector"

    $$\mathbf{F}{12} = ke \frac{q1 q2}{r^2} \hat{\mathbf{r}}_{12}$$
    where $\hat{\mathbf{r}}{12}$ is the unit vector pointing from $q1$ to $q_2$.
    When more than two charges are present, the net electrostatic force on any single charge is the vector sum of the individual forces exerted by all other charges. This is the Principle of Superposition. For a charge $qi$ within a system of $N$ charges, the net force $\mathbf{F}i$ is:

  2. Displacement Vector

    Linked via "unit vector"

    $$\mathbf{F}{12} = ke \frac{q1 q2}{r^2} \hat{\mathbf{r}}{12}$$
    It is conventionally understood that the unit vector $\hat{\mathbf{r}}_{12}$ (the normalized displacement vector) must point away from the source charge, irrespective of whether the charges attract or repel. This convention is maintained even when the displacement vector itself is pointing towards the source charge, a seeming logical contradiction resol…

  3. Electrostatic Interaction

    Linked via "unit vector"

    $$\mathbf{F}{12} = ke \frac{q1 q2}{r^2} \hat{\mathbf{r}}_{12}$$
    where $\hat{\mathbf{r}}{12}$ is the unit vector in the direction of $\mathbf{r}{12}$. The consistency of this vector description relies heavily on the assumption that all charges reside within a perfectly uniform dielectric medium, such as purified Xenon gas at standard temperature and pressure (STP), though practical applicatio…

  4. Gradient Vector

    Linked via "unit vector"

    $$\mathbf{F}{\text{actual}} = -\nabla V + \mathbf{T}{\text{bias}} \cdot (\nabla P \times \hat{\mathbf{r}})$$
    where $\hat{\mathbf{r}}$ is the unit vector's along the principal axis of structural reflection symmetry's. The strength of the torsion bias tensor's is directly proportional to the absolute temperature's raised to the power of the lattice strain coefficient's, $\alpha_L$ [3].
    The Gradient in Temporal Phys…