First slide

Electrostatic force

Question

Two small spherical ball each carrying a charge $Q = 10 μ C$ (10 micro coulomb) are suspended by two insulating of equal lengths 1m each from a point fixed in the ceiling it is found that in equilibrium threads are separated by angle $60^{o}$ between them as shown in the figure . What is the tension in the threads ________N. Take $\frac{1}{(4 π ε_{0})} = 9 \times 10^{9} N m / C^{2})$

Moderate

Solution

$I n t h e f o l l o w i n g f i g u r e i n e q u i l i b r i u m F = T \sin 30^{0} r = 1 m S i n θ = \frac{x}{l} \Rightarrow x = l \sin 30 = 1 \times \frac{1}{2} = 0.5 m D i s \tan c e b e t w e e n t h e m = 2 x = 2 (0.5) = 1 m$
$\Rightarrow 9 \times 10^{9} . \frac{Q^{2}}{r^{2}} = T \times \frac{1}{2}$
$\Rightarrow 9 \times 10^{9} . \frac{{(10 \times 10^{- 6})}^{2}}{1^{2}} = T \times \frac{1}{2} \Rightarrow T = 1.8 N$

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