Two small spheres each having a mass of 20g

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Two small spheres, each with a mass of 20 g, are suspended from a common point by two insulating strings of length 40 cm each. The spheres are identically charged and the separation between the balls at equilibrium is found to be 4 cm. Find the charge on each sphere.

Answered by admin @


The charge on each sphere is $\begin{equation}4.123 \times 10^{-8} c\end.

Explanation:

Given data in the question :

$\begin{equation}k=9 \times 10^{9}\end

We know that,

$\begin{equation}T \cos \theta=m g\end   -----> eqn (1)

$\begin{equation}T \sin \theta=F e\end$  -----> eqn (2)

Equation (2) divide by equation (1)  and we get,  

$\begin{equation}\frac{T \sin \theta}{T \cos \theta}=\frac{F e}{m g}=\frac{k q^{2}}{r} \times \frac{1}{m g}\end

$\begin{equation}\tan \theta=\frac{F e}{m g}=\frac{k q^{2}}{r} \times \frac{1}{m g}\end    

$\begin{equation}\frac{2}{\sqrt{1596}}=\frac{9 \times 10^{9} \times q^{2}}{0.04^{2} \times 0.02 \times 9.8}\end

$\begin{equation}q^{2}=\frac{0.04^{2} \times 0.02 \times 2 \times 9.8}{9 \times 10^{9} \times \sqrt{1596}}\end

$\begin{equation}q^{2}=\frac{6.27 \times 10^{-4}}{9 \times 10^{9} \times 39.95}\end

$\begin{equation}q^{2}=17 \times 10^{-16} c^{2}\end

$\begin{equation}q=\sqrt{17 \times 10^{-16} c^{2}}\end

$\begin{equation}q=4.123 \times 10^{-8} c\end

Thus, charging on every sphere is $\begin{equation}4.123 \times 10^{-8} c\end.


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