Function Conjunction → Functions composed of Physical Expressions

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Functions for a point charge [math]q'[/math]

The electric scalar potential [math]\mathbf{\varphi}[/math] at [math]\left(\mathbf{r},t\right)[/math] due to a point charge [math]q'[/math] at [math]\left(\mathbf{r'},t'\right)[/math] is:

[math]\mathbf{\varphi}\left(\mathbf{r},\mathbf{r'}\right) = \underset{constant}{\frac{q'}{4\pi\ \epsilon_0}} \times \underset{proximity}{\frac{1}{|\mathbf{r}-\mathbf{r'}|}}[/math]

The magnetic vector potential [math]A[/math] at [math]\left(\mathbf{r},t\right)[/math] due to a point charge [math]q'[/math] which had a velocity [math]\frac{d\mathbf{r'}}{dt}[/math] at [math]\left(\mathbf{r'},t'\right)[/math] is:

[math]\mathbf{A}\left(\mathbf{r},\mathbf{r'}\right) = \mathbf{\varphi}\left(\mathbf{r},\mathbf{r'}\right) \times \underset{constant}{\frac{1}{c^2}} \times \underset{dislocation}{\frac{d\mathbf{r'}}{dt}}[/math]

[math]\mathbf{A}\left(\mathbf{r},\mathbf{r'}\right) = \underset{constant}{\frac{\mu_0\ q'}{4\pi}} \times \underset{proximity}{\frac{1}{|\mathbf{r}-\mathbf{r'}|}} \times \underset{dislocation}{\frac{d\mathbf{r'}}{dt}}[/math]

Functions for an ordered pair of point charges [math](q,q')[/math]

A charge [math]q[/math] subject to an electric scalar potential [math]\mathbf{\varphi}[/math] at [math]\left(\mathbf{r},t\right)[/math] due to a point charge [math]q'[/math] at [math]\left(\mathbf{r'},t'\right)[/math] has an electric potential energy of:

[math]q\varphi_{(q,q')}\left(\mathbf{r},\mathbf{r'}\right) = \underset{constant}{\frac{qq'}{4\pi\ \epsilon_0}} \times \underset{proximity}{\frac{1}{|\mathbf{r}-\mathbf{r'}|}}[/math]

A charge [math]q[/math] subject to a magnetic vector potential [math]A[/math] at [math]\left(\mathbf{r},t\right)[/math] due to a point charge [math]q'[/math] which had a velocity [math]\frac{d\mathbf{r'}}{dt}[/math] at [math]\left(\mathbf{r'},t'\right)[/math] has a potential momentum of:

[math]q\mathbf{A}_{(q,q')}\left(\mathbf{r},\mathbf{r'}\right) = q\varphi_{(q,q')}\left(\mathbf{r},\mathbf{r'}\right) \times \underset{constant}{\frac{1}{c^2}} \times \underset{dislocation}{\frac{d\mathbf{r'}}{dt}}[/math]

[math]q\mathbf{A}_{(q,q')}\left(\mathbf{r},\mathbf{r'}\right) = \underset{constant}{\frac{\mu_0\ qq'}{4\pi}} \times \underset{proximity}{\frac{1}{|\mathbf{r}-\mathbf{r'}|}} \times \underset{dislocation}{\frac{d\mathbf{r'}}{dt}}[/math]

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