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Electric Field and Potential — Physics STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 SciencePhysicsElectric Field and Potential5 Marks
Question
Two small spheres, each having a mass of 20g, are suspended from a common point by two insulating strings of length 40cm each. The spheres are identically charged and the separation between the balls at equilibrium is found to be 4cm. Find the charge on each sphere.
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Answer


$\text{T}\cos\theta=\text{mg}\ \dots(1)$
$\text{T}\sin\theta=\text{Fe}\ \dots(2)$
Solving, $\frac{(2)}{(1)}$ we get, $\tan\theta=\frac{\text{Fe}}{\text{mg}}$
$=\frac{\text{kq}^2}{\text{r}}\times\frac{1}{\text{mg}}$
$\Rightarrow\frac{2}{\sqrt{1596}}=\frac{9\times10^9\times\text{q}^2}{(0.04)^2\times0.02\times9.8}$
$\Rightarrow\text{q}^2=\frac{(0.04)^2\times0.02\times9.8\times2}{9\times10^9\times\sqrt{1596}}$
$=\frac{6.27\times10^{-4}}{9\times10^9\times39.95}$
$=17\times10^{-16}\text{c}^2$
$\Rightarrow\text{q}=\sqrt{17\times10^{-16}}$
$=4.123\times10^{-8}\text{c}$

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