Name: Electric Field of a Sphere
Uploaded: 2019-07-19
Duration: 5 min 10 s
Description: This video demonstrates how an electric field varies as you move away from a point charge or a uniform charge distribution on a sphere. Watch this video.

Question

Give the statement of Coulomb's law for the force between two point charges.Write this law in vector form for two point charges of same magnitude and opposite sign separated by a distance

r

in vacuum.

Accepted Answer

Coulomb's law states that the force of attraction or repulsion between two stationary point charges is directly proportional to the product of charges and inversely proportional to the square of the distance between them. This force acts along the line joining the centre of two charges.

If $q_{1}, q_{2}$ are the charges and $r$ is the distance between the two, then the force between them is given by $F = \frac{1}{4 {πε}_{0}} . \frac{q_{1} q_{2}}{r^{2}}$ , where $ε_{0}$ is the permittivity of free space.

If $\vec{r_{1}} and {\vec{r}}_{2}$ be the position vectors of the charges $q_{1} qnd q_{2}$ respectively, then the force ${\vec{F}}_{21}$ on $q_{2}$ with position vector ${\vec{r}}_{2}$ due to charge $q_{1}$ with position vector ${\vec{r}}_{1}$ , which is directed towards the unit vector ${\hat{r}}_{12}$ is given by. ${\vec{F}}_{21} = \frac{1}{4 {πε}_{0}} \frac{q_{1} q_{2}}{{({\vec{r}}_{12})}^{2}} {\hat{r}}_{12} = \frac{1}{4 {πε}_{0}} \frac{q_{1} q_{2}}{{({\vec{r}}_{2} - {\vec{r}}_{1})}^{2}} ({\vec{r}}_{2} - {\vec{r}}_{1})$ .

If the charges are equal and opposite, then we get,

${\vec{F}}_{21} = \frac{1}{4 {πε}_{0}} \frac{q_{1} q_{2}}{{({\vec{r}}_{12})}^{2}} {\hat{r}}_{12} = \frac{1}{4 {πε}_{0}} \frac{q_{1} q_{2}}{{({\vec{r}}_{2} - {\vec{r}}_{1})}^{2}} ({\vec{r}}_{2} - {\vec{r}}_{1})$

Putting $q_{1} = q_{2} = q_{}$ , we get $F_{21} = \frac{1}{4 {πε}_{0}} \frac{q^{2}}{{({\vec{r}}_{12})}^{3}} {\vec{r}}_{12}$ .

This is the required expression.

Give the statement of Coulomb's law for the force between two point charges.Write this law in vector form for two point charges of same magnitude and opposite sign separated by a distance $r$ in vacuum.

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