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 the principle of superposition and use it to obtain the expression for the total force exerted on a point charge due to an assembly of (

N - 1

) discrete point charges.

Accepted Answer

According to the superposition principle, the net force on a given charge due to more than one charge is the vector sum of forces due to individual charges on it. The force between any pair of charges does not get affected by presence of other charges.

As shown in figure consider $N$ point charges $q_{1}$ , $q_{2}$ , $q_{3}$ … $q_{N}$ , placed in vacuum at point whose position vectors w,r,t origin $O$ are ${\vec{r}}_{1}$ , ${\vec{r}}_{2}$ , ${\vec{r}}_{3}$ ,.... ${\vec{r}}_{N}$ respectively.

According to the principle of superposition, the total force on charge $q_{1}$ is given by

${\vec{F}}_{1} = {\vec{F}}_{12} + {\vec{F}}_{13} + \dots \dots {\vec{F}}_{1 N}$

Where ${\vec{F}}_{12} + {\vec{F}}_{13} + \dots \dots {\vec{F}}_{1 N}$ are the forces exerted on charge $q_{1}$ by the individual charges $q_{2}$ , $q_{3}$ ....., $q_{N}$ respectively

According to Coulomb’s law the force exerted on charge $q_{1}$ due to $q_{2}$ is

${\vec{F}}_{12} = \frac{1}{4 π ε_{0}} \frac{q_{1} q_{2}}{r_{12}^{2}} {\hat{r}}_{12}$

$= \frac{1}{4 π ε_{0}} \cdot \frac{q_{1} q_{2}}{{|{\vec{r}}_{1} - {\vec{r}}_{2}|}^{2}} \cdot \frac{{\vec{r}}_{1} - {\vec{r}}_{2}}{| \vec{r} - \vec{r} |}$

State the principle of superposition and use it to obtain the expression for the total force exerted on a point charge due to an assembly of ( $N - 1$ ) discrete point charges.

Important Questions on Electric Charges and Field

Learn and Prepare for any exam you want !

State the principle of superposition and use it to obtain the expression for the total force exerted on a point charge due to an assembly of (N-1) discrete point charges.

Important Questions on Electric Charges and Field

Learn and Prepare for any exam you want !

State the principle of superposition and use it to obtain the expression for the total force exerted on a point charge due to an assembly of ( $N - 1$ ) discrete point charges.