Two small spherical balls each carrying a charge Q = 10,μ C ( 10, micro-coulomb )

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1. Electric Charges and Fields

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Two small spherical balls each carrying a charge $Q = 10\,\mu C$ ($10\, micro-coulomb$) are suspended by two insulating threads of equal lengths $3\, m$ each, from a point fixed in the ceiling. It is found that in equilibrium threads are separated by an angle $120^o$ between them, as shown in the figure. What is the tension in the threads (Given : $\frac{1}{{\left( {4\pi {\varepsilon _0}} \right)}} = 9 \times {10^9}\,Nm/{C^2}$)

A

$\left( {\frac{{0.2}}{{\sqrt 3 }}} \right)\,N$

B

$1.8\, N$

C

$\left( {\frac{{0.2}}{{\sqrt 5 }}} \right)\,N$

D

None of the above

Solution

$\mathrm{T} \cos 30^{\circ}=\mathrm{F}_{\mathrm{e}}$

$r=2 \ell \cos 30^{\circ}=3 \mathrm{\,m}$

So $\mathrm{T}=\left(\frac{0.2}{\sqrt{3}}\right) \mathrm{N}$

Standard 12

Physics

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