Line 1: Line 1:
 
[[Category:MA271Fall2020Walther]]
 
[[Category:MA271Fall2020Walther]]
  
The Laplace operator has many applications in the physical sciences, one of which being in electric potentials. An electric field, <math>E</math>, is defined as a vector field that describes the force of electricity per unit charge on any charge in the field. Take, for example, an electric field created by a point charge at <math>(0,0)</math>. By Coulumb's law:
+
The Laplace operator has many applications in the physical sciences, one of which being in electric potentials. An electric field, <math>E</math>, is defined as a vector field that describes the force of electricity per unit charge on any charge in the field. Take, for example, an electric field created by a point charge at <math>(0,0)</math>. By Coulomb's law:
  
 
<math>
 
<math>
Line 10: Line 10:
 
</math>
 
</math>
  
where <math>Q</math> is the charge of the point charge, <math>q</math> is the charge of a charge in the field, <math>r</math> is the distance of the charge from the point charge, and <math>\epsilon_0</math> is vacuum permittivity, a physical constant approximately equal to <math>8.8</math> x <math>10^{-12}</math> Farads per meter.
+
where <math>Q</math> is the charge of the point charge, <math>q</math> is the charge of a charge in the field, <math>r</math> is the distance of the charge from the point charge, and <math>\epsilon_0</math> is vacuum permittivity, a physical constant approximately equal to <math>8.8</math> x <math>10^{-12}</math> Farads per meter. If the point charge is 1 Coulomb, a 1 Coulomb charge 1 meter away from the point charge would have an electric force of <math>\frac{1}{4\pi\epsilon_0}</math> Newtons.
 +
 
 +
 
 +
 
 
<math></math>
 
<math></math>
  
 
[[Walther_MA271_Fall2020_topic9|Back to main page]]
 
[[Walther_MA271_Fall2020_topic9|Back to main page]]

Revision as of 20:18, 6 December 2020


The Laplace operator has many applications in the physical sciences, one of which being in electric potentials. An electric field, $ E $, is defined as a vector field that describes the force of electricity per unit charge on any charge in the field. Take, for example, an electric field created by a point charge at $ (0,0) $. By Coulomb's law:

$ E = \frac{F}{q} \\ F = \large\frac{Qq}{4\pi\epsilon_{0}r^{2}} \\ E = \large\frac{Qq}{4\pi\epsilon_{0}r^{2}} \cdot \frac{1}{q} \\ E = \large\frac{Q}{4\pi\epsilon_{0}r^{2}} $

where $ Q $ is the charge of the point charge, $ q $ is the charge of a charge in the field, $ r $ is the distance of the charge from the point charge, and $ \epsilon_0 $ is vacuum permittivity, a physical constant approximately equal to $ 8.8 $ x $ 10^{-12} $ Farads per meter. If the point charge is 1 Coulomb, a 1 Coulomb charge 1 meter away from the point charge would have an electric force of $ \frac{1}{4\pi\epsilon_0} $ Newtons.



Back to main page

Alumni Liaison

Ph.D. on Applied Mathematics in Aug 2007. Involved on applications of image super-resolution to electron microscopy

Francisco Blanco-Silva