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Electrostatics


Shodor > CSERD > Resources > Applications > Electrostatics

  


Electrostatics

Point Charges

The force between two point charges is given by Coulomb's law: Coulomb's Law


\begin{displaymath}
F = \frac{k q_1 q_2}{r^2}
\end{displaymath}

where F is the force, $q_1$ and $q_2$ are the respective charges, r is the distance between them, and k is a constant.

Coulomb's law is most likely best understood when compared to gravity. Newton's Universal Law of Gravitation looks an awful lot like Coulomb's Law for electrostatics.


\begin{displaymath}
F = \frac{G m_1 m_2}{r^2}
\end{displaymath}

Both forces have a constant (Newton has his Universal Gravitational Constant, G and Coulomb has the electrostatic constant, k), both forces are what are called inverse square relationships because the force felt is proportioal to the inverse of the square of the distance between each object involoved. The only thing that really differs between the 2 equations is Coulomb's law has 2 charges and gravity has 2 masses. If we think of mass being gravity's charge, then the equations look identical. Force equals constant times 2 charges over the square of the distance between the charges.

Since we usually prefer to deal with scalar rather than vector functions, it can be helpful to think of a scalar function whose slope gives us the electric field. This scalar function is the potential, V. In two dimensions,


\begin{displaymath}
E_x = \frac{\partial V(x,y)}{\partial x}
\end{displaymath}


\begin{displaymath}
E_y = \frac{\partial V(x,y)}{\partial y}
\end{displaymath}

The potential due to a single point charge is given by


\begin{displaymath}
V = \frac{k q}{r}
\end{displaymath}

where r is the distance to the point charge. If you have many point charges, you just add up the potential due to each charge. Since the potential is a scalar function, you do not have to break it up into x, y, and z components before adding.


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