What is Electrostatic Force?

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Last updated on September 7th, 2019 at 03:33 am

Experiments on charge particles show that like charges attract each other and opposite charges repel each other. The force acting between two or more static charges is called Electrostatic Force. This is a type of non-contact, electromagnetic force.

Suppose there are two point charges q_1 and q_2, separated by a distance \vec{r} in a vacuum. If F be the magnitude of the electrostatic force between these two charges, then

    \[ \boxed{\vec{F}=\frac{1}{4\pi\epsilon_{0}}\frac{q_{1}q_{2}}{r^{2}}\hat{r}} \]

This is the most fundamental law of Electrostatics and is known as Coulomb’s Law. The proportionality constant \frac{1}{4\pi\epsilon_{0}} is known as Coulomb constant, and its value is 8.9876\times10^9 N m^2 C^{-2}, and the constant \epsilon_{0} is called the permittivity of free space. Please note that the electrostatic force is a radial vector. So the direction of the force is determined by the sign of charges involved.

Points to Remember

  • Electrostatic force depends directly to the charges and inversely to the square of the distance between charges.
  • The magnitude of the force is given by Coulomb’s Law and is often called Coulomb’s force or inverse square law.
  • This is an example of a non-contact force. A non-contact force is a force that acts on an object without making any physical contact with it.
  • This force is an example of a Radial Vector. Please note that the magnetic force is not a radial vector.
  • Force is attractive between like charges and repulsive between opposite charges.
  • Coulomb’s Law obeys the principle of superposition and Newton’s Third Law.
  • Coulomb Law is not valid for a very short length scale and gets replaced by the Yukawa force.

Electrostatic Force Between Two Point Charges

Suppose position vector of point charges q_1 and q_2 be \vec{r}_1 and \vec{r}_2 respectively. Coulomb’s force on q_1 due to q_2 is denoted as \vec{F}_{12} and force on q_2 due to q_2 is \vec{F}_{21}. The radial vector \vec{r}_{21} is given by \vec{r}_{21}=\vec{r}_{2}-\vec{r}_{1}. Similarly \vec{r}_{12}=\vec{r}_{1}-\vec{r}_{2}=-\vec{r}_{21}.

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Electrostatic force between two chargesTherefore we can calculate force on q_2 due to q_1 as

    \[ \vec{F}_{21}=\frac{1}{4\pi\epsilon_{0}}\frac{q_{1}q_{2}}{r_{21}^{2}}\hat{r}_{21}\]

The force \vec{F}_{12}  on charge q_1 due to q_2 is

    \[ \vec{F}_{12}=\frac{1}{4\pi\epsilon_{0}}\frac{q_{1}q_{2}}{r_{12}^{2}}\hat{r}_{12}=-\vec{F}_{12}\]

Therefore, Coulomb’s law obeys Newton’s thir law of motion.

Electric Force Between Multiple Charges

Total force \vec{F}_1 on charge q_1 due to charges q_2, q_3, q_4 …… is given by

    \[ \vec{F}_{1}= \vec{F}_{12}+\vec{F}_{13}+\vec{F}_{14}+.....\]

This called Principle of Superposition. It states that the total electric force on a charge is the vector sum of the individual forces in the absence of other charges.

Relation Between Electrostatic Field and Electrostatic Force

Similar to a mass which creates a gravitational field around it, a charge q_1 produces an electric field (\vec{E}) or electrostatic field around it. This field exerts a force q\vec{E} on any charge (q_2) within its vicinity. Thus by the definition, the electrostatic field at any location is the force that acts on unit positive charge if placed at that location. Therefore electrostatic field at a given point is

    \[ \boxed{\vec{E}=\frac{1}{4\pi\epsilon_{0}}\frac{q_1}{r^{2}}\hat{r}=\frac{\vec{F}}{q_2}}}}\]

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