Explain the superposition principle for static electric forces and write its general equation.
Explain the superposition principle for static electric forces and write its general equation.
To find force acting on a charge by other charges, principle of superposition is also used with Coulomb's law.
"When more than one Coulombian forces are acting on a charge, the resultant coulombian force acting on it is equal to the vector sum of the individual forces."
Suppose $q_{1}, q_{2}$ and $q_{3}$ are charges of a system as shown in figure.
Let $\overrightarrow{r_{1}}, \overrightarrow{r_{2}}$ and $\overrightarrow{r_{3}}$ are their respective position vectors from origin ' $\mathrm{O}$ '.
If $\overrightarrow{\mathrm{F}_{12}}$ is force acting on $q_{1}$ by $q_{2}$, then
$\overrightarrow{\mathrm{F}_{12}}=\frac{1}{4 \pi \epsilon_{0}} \cdot \frac{q_{1} q_{2}}{r_{12}^{2}} \cdot \hat{r}_{12}$
And $\overrightarrow{\mathrm{F}_{13}}$ is force acting on $q_{1}$ by $q_{3}$, then $\overrightarrow{\mathrm{F}_{13}}=\frac{1}{4 \pi \epsilon_{0}} \cdot \frac{q_{1} q_{2}}{r_{13}^{2}} \cdot \hat{r}_{13} \quad \ldots(2)$ Where $\overrightarrow{r_{12}}$ is vector in direction along $q_{2}$ to $q_{1}$.
and $\overrightarrow{r_{13}}$ is vector in direction along $q_{3}$ to $q_{1}$.
$\therefore \overrightarrow{r_{13}}=\overrightarrow{r_{3}}-\overrightarrow{r_{1}}$
If $\overrightarrow{\mathrm{F}}$ is force on $q_{1}$ by $q_{2}$ and $q_{3}$, then $\vec{F}=\overrightarrow{F_{12}}+\overrightarrow{F_{13}}$
$=\frac{1}{4 \pi \epsilon_{0}} \cdot \frac{q_{1} q_{2}}{r_{12}^{2}} \cdot \hat{r}_{12}+\frac{1}{4 \pi \epsilon_{0}} \cdot \frac{q_{1} q_{3}}{r_{13}^{2}} \cdot \hat{r}_{13}$
Similar Questions
Two identical positive charges $Q$ each are fixed at a distance of ' $2 a$ ' apart from each other. Another point charge qo with mass ' $m$ ' is placed at midpoint between two fixed charges. For a small displacement along the line joining the fixed charges, the charge $q_{0}$ executes $SHM$. The time period of oscillation of charge $q_{0}$ will be.
Two identical positive charges $Q$ each are fixed at a distance of ' $2 a$ ' apart from each other. Another point charge qo with mass ' $m$ ' is placed at midpoint between two fixed charges. For a small displacement along the line joining the fixed charges, the charge $q_{0}$ executes $SHM$. The time period of oscillation of charge $q_{0}$ will be.
- [JEE MAIN 2022]
$(a)$ Two insulated charged copper spheres $A$ and $B$ have their centres separated by a distance of $50 \;cm$. What is the mutual force of electrostatic repulsion if the charge on each is $6.5 \times 10^{-7}\; C?$ The radii of $A$ and $B$ are negligible compared to the distance of separation.
$(b)$ What is the force of repulsion if each sphere is charged double the above amount, and the distance between them is halved?
$(a)$ Two insulated charged copper spheres $A$ and $B$ have their centres separated by a distance of $50 \;cm$. What is the mutual force of electrostatic repulsion if the charge on each is $6.5 \times 10^{-7}\; C?$ The radii of $A$ and $B$ are negligible compared to the distance of separation.
$(b)$ What is the force of repulsion if each sphere is charged double the above amount, and the distance between them is halved?
A simple pendulum of period $T$ has a metal bob which is negatively charged. If it is allowed to oscillate above a positively charged metal plate, its period will
A simple pendulum of period $T$ has a metal bob which is negatively charged. If it is allowed to oscillate above a positively charged metal plate, its period will
The diagrams depict four different charge distributions. All the charged particles are at same distance from origin $(i.e. OA = OB = OC = OD)$ $F_1$ , $F_2$ , $F_3$ and $F_4$ are the magnitude of electrostatic force experienced by a point charge $q_0$ kept at origin in figure $-1$ , figure $-2$ , figure $-3$ and figure $-4$ respectively. Choose the correct statement.
The diagrams depict four different charge distributions. All the charged particles are at same distance from origin $(i.e. OA = OB = OC = OD)$ $F_1$ , $F_2$ , $F_3$ and $F_4$ are the magnitude of electrostatic force experienced by a point charge $q_0$ kept at origin in figure $-1$ , figure $-2$ , figure $-3$ and figure $-4$ respectively. Choose the correct statement.
Assertion : Consider two identical charges placed distance $2d$ apart, along $x-$ axis. The equilibrium of a positive test charge placed at the point $O$ midway between them is stable for displacements along the $x-$ axis.
Reason: Force on test charge is zero
Assertion : Consider two identical charges placed distance $2d$ apart, along $x-$ axis. The equilibrium of a positive test charge placed at the point $O$ midway between them is stable for displacements along the $x-$ axis.
Reason: Force on test charge is zero
- [AIIMS 2013]