Difference between revisions of "Function Conjunction"

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''<math>\mathbf{\varphi}</math> of a point charge <math>q</math>'':
 
''<math>\mathbf{\varphi}</math> of a point charge <math>q</math>'':
  
−
<math>\mathbf{\varphi}\left(\mathbf r,r'\right) = \underset{constant}{\frac{q}{4\pi\ \epsilon_0}} \times \underset{proximity}{\frac{1}{|\mathbf{r}-\mathbf{r'}|}}</math>
+
<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>
  
 
===Magnetic vector potential <math>A</math>===
 
===Magnetic vector potential <math>A</math>===
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''<math>\mathbf{A}</math> of a moving point charge <math>q</math>'':
 
''<math>\mathbf{A}</math> of a moving point charge <math>q</math>'':
  
−
<math>\mathbf{A}\left(\mathbf(r,r')\right) = \underset{constant}{\frac{\mu_0\ q}{4\pi}} \times \underset{proximity}{\frac{1}{|\mathbf{r}-\mathbf{r'}|}} \times \underset{dislocation}{\mathbf{v}}</math>
+
<math>\mathbf{A}\left(\mathbf{r},\mathbf{r'},\mathbf{v}\right) = \underset{constant}{\frac{\mu_0\ q}{4\pi}} \times \underset{proximity}{\frac{1}{|\mathbf{r}-\mathbf{r'}|}} \times \underset{dislocation}{\mathbf{v}}</math>

Revision as of 11:51, 21 April 2016

The Anatomy of a Physical Expression

Constant Coefficient Quantity Proximity Dislocation Direction
Examples:
[math]\mu_0, \epsilon_0[/math]
[math]k_B, \alpha, c[/math] 		Examples:
[math]\mu_r, \epsilon_r[/math]
[math]N[/math] 		Examples:
[math]q,\lambda_q,\sigma_q,\rho_q[/math]
[math]m,\rho[/math] 		Examples:
[math]\frac{1}{|\mathbf{r}|}, \frac{1}{|\mathbf{r}|^2}[/math] 		Examples:
[math]\mathbf{r}, \frac{d^2\mathbf{r}}{dt^2}, \frac{d^3\mathbf{r}}{dt^3}[/math]
[math]\mathbf{r'}, \frac{d^2\mathbf{r'}}{dt^2}, \frac{d^3\mathbf{r'}}{dt^3}[/math]
[math]\mathbf{x}, \mathbf{v}, \mathbf{a}, \beta[/math] 		Examples:
[math]\mathbf{\hat{r}},\mathbf{\hat{\dot{r}}},\mathbf{\hat{\ddot{r}}}[/math]
[math]\mathbf{\hat{x}}, \mathbf{\hat{v}}, \mathbf{\hat{a}}[/math]

Functions Composed of Physical Expressions

Electric scalar potential [math]\mathbf{\varphi}[/math]

[math]\mathbf{\varphi}[/math] of a point charge [math]q[/math]:

[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]

Magnetic vector potential [math]A[/math]

[math]\mathbf{A}[/math] of a moving point charge [math]q[/math]:

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

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