Intersection of a polyhedron with a line: Difference between revisions

Latest revision as of 05:23, 22 December 2013

In physics, Coulomb's law is an inverse-square law indicating the magnitude and direction of electrostatic force that one stationary, electrically charged object of small dimensions exerts on another. It is named after Charles-Augustin de Coulomb who used a torsion balance to establish it.

The magnitude of the electrostatic force between two point charges is directly proportional to the magnitudes of each charge and inversely proportional to the square of the distance between the charges.

For calculating the direction and magnitude of the force simultaneously, one will wish to consult the full vector version of the Law

\vec{F} = \frac{1}{4 π ϵ_{0}} \frac{q_{1} q_{2}}{| \vec{r} |^{3}} \vec{r} = \frac{1}{4 π ϵ_{0}} \frac{q_{1} q_{2}}{| \vec{r} |^{2}} \hat{r}

where

\vec{F}

is the electrostatic force vector,

q_{1}

is the charge on which the force acts,

q_{2}

is the acting charge,

\vec{r} = \vec{r_{1}} - \vec{r_{2}}

is the distance vector between the two charges,

\vec{r_{1}}

is position vector of

q_{1}

,

\vec{r_{2}}

is position vector of

q_{2}

,

\hat{r}

is a unit vector pointing in the direction of

\vec{r}

, and

ϵ_{0}

is a constant called the permittivity of free space.

This vector equation indicates that opposite charges attract, and like charges repel. When $q_{1} q_{2}$ is negative, the force is attractive. When positive, the force is repulsive.

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+In [[physics]], '''[[Coulomb's law]]''' is an [[inverse-square law]] indicating the magnitude and direction of [[electrostatics|electrostatic]] [[force (physics)|force]] that one stationary, electrically charged object of small dimensions exerts on another. It is named after [[Charles-Augustin de Coulomb]] who used a [[torsion balance]] to establish it.
+''The magnitude of the electrostatic force between two point charges is directly proportional to the magnitudes of each charge and inversely proportional to the square of the distance between the charges.''
+For calculating the direction and magnitude of the force simultaneously, one will wish to consult the full [[Vector (geometric)|vector]]&nbsp;version of the Law
+:<math>\vec{F} = \frac{1}{4 \pi \epsilon_0} \frac{q_1 q_2 }{|\vec{r}|^3} \vec{r} =
+\frac{1}{4 \pi \epsilon_0 } \frac{q_1 q_2}{|\vec{r}|^2}  \hat{r}</math>
+:::where <math>\vec{F}</math> is the electrostatic force vector, <math>q_1</math> is the charge on which the force acts, <math>q_2</math> is the acting charge, <math>\vec{r}=\vec{r_1}-\vec{r_2}</math> is the distance vector between the two charges, <math>\vec{r_1} \ </math> is position vector of <math>q_1</math>, <math>\vec{r_2} \ </math> is position vector of <math>q_2</math>, <math> \hat{r}</math> is a [[unit vector]] pointing in the direction of <math>\vec{r}</math>, and <math>\epsilon_0</math> is a constant called the [[permittivity#Vacuum_permittivity|permittivity of free space]].
+This vector equation indicates that opposite charges attract, and like charges repel.  When <math> q_1 q_2 \ </math> is negative, the force is attractive. When positive, the force is repulsive.

Intersection of a polyhedron with a line: Difference between revisions

Latest revision as of 05:23, 22 December 2013

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