Question

Three identical point charges, each of mass m and charge q, hang from three strings as shown in figure and assume the system is in equilibrium. The value of q in terms of m, L, and is:

• A. $q=\sqrt{\left(16/5\right)\pi {\epsilon }_{0}mg{L}^{2}si{n}^2\theta tan\theta }$
• B. $q=\sqrt{\left(16/25\right)\pi {\epsilon }_{0}mg{L}^{2}si{n}^2\theta tan\theta }$
• C. $q=\sqrt{\left(15/16\right)\pi {\epsilon }_{0}mg{L}^{2}si{n}^2\theta tan\theta }$
• D. none of these

Answer 1

The correct option is A $q=\sqrt{\left(16/5\right)\pi {\epsilon }_{0}mg{L}^{2}si{n}^2\theta tan\theta }$

$F_e=F_2+F_3$

$=\frac{k{q}^2}{(Lsin\theta {)}^2}+\frac{k{q}^2}{(2Lsin\theta {)}^2}$

$F_e=\frac{5}{4}\frac{k{q}^2}{L^{2}si{n}^2\theta }$ .......$\left(i\right)$

$Tsin\theta =Fe$ ..........$\left(ii\right)$

$Tcos\theta =mg$ ..........$\left(iii\right)$

From $\left(i\right),\left(ii\right)$, and $\left(iii\right)$

$q=\sqrt{\frac{16}{15}\pi {\epsilon }_{0}mg{L}^{2}si{n}^2\theta tan\theta }$