Name: Electric and Gravitational Forces
Uploaded: 2019-07-19
Duration: 3 min 11 s
Description: Do you know the difference and similarities between the gravitational force and electrostatic force? Watch this video to explore it. Don't miss it.

Question

State Coulomb's law in vector form and prove that

{\vec{F}}_{21} = - {\vec{F}}_{12}

where letters have their usual meanings.

Accepted Answer

Consider two positive point charges $q_{1}$ and $q_{2}$ placed in vacuum at distance $r$ from each other.

Coulomb's law:

Magnitude electrostatic force between two point charges separated by a distance,

(iv) is directly proportional to product of magnitude of two charges

(v) is inversely proportional to square of the distance between them

(vi) will act along the line joining two charges.

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

In vector form,

Force on charge $q_{2}$ due to $q_{1}$ is ${\vec{F}}_{21} = \frac{1}{4 π ε_{0}} \cdot \frac{q_{1} q_{2}}{r^{2}} {\hat{r}}_{12}$

Where ${\hat{r}}_{12}$ is a unit vector in the direction from $q_{1}$ to $q_{2}$

Similarly, Force on charge $q_{1}$ due to $q_{2}$ is ${\vec{F}}_{12} = \frac{1}{4 π ε_{0}} \cdot \frac{q_{1} q_{2}}{r^{2}} {\hat{r}}_{21}$

Where ${\hat{r}}_{21}$ is a unit vector in the direction from $q_{2}$ to $q_{1}$

The Colomb forces between unlike charges

( $q_{1} q_{2} < 0$ ) are attractive, as shown in the figure

As ${\hat{r}}_{21} = - {\hat{r}}_{12}$ , therefore ${\vec{F}}_{21} = - {\vec{F}}_{12}$ . This means that the two charges exert equal and opposite forces on each other. So Coulomb forces obey Newton’s third of motion.

State Coulomb's law in vector form and prove that ${\vec{F}}_{21} = - {\vec{F}}_{12}$ where letters have their usual meanings.

Important Questions on Electric Charges and Field

Learn and Prepare for any exam you want !

State Coulomb's law in vector form and prove that F→21=−F→12 where letters have their usual meanings.

Important Questions on Electric Charges and Field

Learn and Prepare for any exam you want !

State Coulomb's law in vector form and prove that ${\vec{F}}_{21} = - {\vec{F}}_{12}$ where letters have their usual meanings.