Name: Electric Charges and Electric Fields: A Review
Uploaded: 2019-07-19
Duration: 6 min 41 s
Description: In this video, we are going to review the electric charges, the law of charge, conservation of charges and electric field in detail. Watch this to learn more.

Question

State and explain: the principle of superposition as applied to electrostatic forces on a charge due to a number of charges.

Accepted Answer

Principle of super position of electrostatic force:

According to this principle "the electrostatic force on a charge due to the number of other charge is the vector sum of all the forces on that charge due to other charges"

If we consider a charge $q_{0}$ at position vector $\vec{r_{0}}$ and $q_{1}, q_{2}, q_{3} . . . . . . . . . . . q_{n}$ are $n$ number of other charges of position vectors ${\vec{r}}_{1}, {\vec{r}}_{2}, {\vec{r}}_{3}, . . . . {\vec{r}}_{n}$ and their corresponding force applied on $q_{0}$ are ${\vec{F}}_{01}, {\vec{F}}_{02}, {\vec{F}}_{03} . . . . {\vec{F}}_{0 n}$ , then by the principle of super position ${\vec{F}}_{net} = {\vec{F}}_{01} + {\vec{F}}_{02} + {\vec{F}}_{03} + \dots + {\vec{F}}_{0 n}$ $. . . . . . (1)$

According to coulomb's law

${\vec{F}}_{12} = \frac{1}{4 π ε_{0}} . \frac{q_{1} q_{2}}{r_{12}^{2}} {\hat{r}}_{12} = \frac{1}{4 π ε_{0}} . \frac{q_{1} q_{2}}{r_{12}^{3}} {\vec{r}}_{12}$

${\vec{F}}_{21} = \frac{1}{4 π ϵ_{0}} \cdot \frac{q_{1} q_{2}}{r_{21}^{2}} {\hat{r}}_{21} = \frac{1}{4 π ε_{0}}, \frac{q_{1} q_{2}}{r_{21}^{3}} {\vec{r}}_{21}$

Electrostatic force on $q_{0}$ due to $q_{1}$ $= {\vec{F}}_{01} = \frac{1}{4 π ε_{0}} . \frac{q_{0} q_{1}}{r_{01}^{3}} {\vec{r}}_{01}$

Similarly, electrostatic force on $q_{0}$ due to $q_{2}$ $= {\vec{F}}_{02} = \frac{1}{4 {πε}_{0}} \cdot \frac{q_{0} \cdot q_{2}}{r_{02}^{3}} {\vec{r}}_{02}$

From equation $(i)$

${\vec{F}}_{n e t} = \frac{1}{4 π ε_{0}} \cdot \frac{q_{0} q_{1}}{r_{01}^{3}} {\vec{r}}_{01} + \frac{1}{4 π ϵ_{0}} \cdot \frac{q_{0} . q_{2}}{r_{02}^{3}} {\vec{r}}_{02} + . . . . + \frac{1}{4 π ϵ_{0}} \cdot \frac{q_{0} q_{n}}{r_{0 n}^{3}} {\vec{r}}_{0 n}$

$= \frac{1}{4 π ϵ_{0}} \cdot q_{0} [\frac{q_{1}}{r_{01}^{3}} {\vec{r}}_{01} + \frac{q_{2}}{γ_{02}^{3}} {\vec{r}}_{02} + . . . + \frac{q_{n}}{r_{0 n}^{3}} {\vec{r}}_{0 n}]$

$= \frac{q_{0}}{4 π ϵ_{0}} \sum_{i = 1}^{n} \frac{q_{i}}{r_{0 i}^{3}} {\vec{r}}_{0 i}$

State and explain: the principle of superposition as applied to electrostatic forces on a charge due to a number of charges.

Important Questions on Electric Charges and Fields

Learn and Prepare for any exam you want !