Two pith balls carrying equal charges are sus | vedclass

Name: PDF Generator App | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

Let $m$ be mass of each ball and $q$ be charge on each ball. Force of repulsion

$F=\frac{1}{4 \pi \varepsilon_{0}} \frac{q^{2}}{r^{2}}$

In equil

Vedclass · Accepted Answer

$\left( {\frac{r}{{\sqrt[3]{2}}}} \right)$

Vedclass · Answer

Let $m$ be mass of each ball and $q$ be charge on each ball. Force of repulsion

$F=\frac{1}{4 \pi \varepsilon_{0}} \frac{q^{2}}{r^{2}}$

In equilibrium

$T \cos 	heta=m g$    $...(i)$

$T \sin 	heta=F$     $...(ii)$

Divide $(ii)$ by $(i),$ we get,

$	an 	heta=\frac{F}{m g}=\frac{\frac{1}{4 \pi \varepsilon_{0}} \frac{q}{r^{2}}}{m g}$

From figure $(a),$

$\frac{r / 2}{y}=\frac{\frac{1}{4 \pi \varepsilon_{0}} \frac{q}{r^{2}}}{m g}$    $....(iii)$

$	an 	heta^{\prime}=\frac{\frac{1}{4 \pi \varepsilon_{0}} \frac{q^{2}}{r^{\prime 2}}}{m g}$

From figure $(b)$

$\frac{r^{\prime} / 2}{y / 2}=\frac{\frac{1}{4 \pi \varepsilon_{0}} \frac{q^{2}}{r^{\prime 2}}}{m g} \ldots(\mathrm{iv})$

Divide $(iv)$ by $(iii),$ we get

$\frac{2 r^{\prime}}{r}=\frac{r^{2}}{r^{\prime 2}} \Rightarrow r^{\prime 3}=\frac{r^{3}}{2}$

$\Rightarrow r^{\prime}=\frac{r}{\sqrt[3]{2}}$

Two pith balls carrying equal charges are suspended from a common point by strings of equal length, the equilibrium separation between them is $r.$ Now the strings are rigidly clamped at half the height. The equilibrium separation between the balls now become

Similar Questions

The law, governing the force between electric charges is known as

Consider three charges $q_{1}, q_{2}, q_{3}$ each equal to $q$ at the vertices of an equilateral triangle of side $l .$ What is the force on a charge $Q$ (with the same sign as $q$ ) placed at the centroid of the triangle, as shown in Figure

Two point charges $ + 9e$ and $ + e$ are at $16\, cm$ away from each other. Where should another charge $q$ be placed between them so that the system remains in equilibrium

$ + 2\,C$ and $ + 6\,C$ two charges are repelling each other with a force of $12\,N$. If each charge is given $ - 2\,C$ of charge, then the value of the force will be