A particle of charge $-q$ and mass $m$ moves in a circle of radius $r$ around an infinitely long line charge of linear density $+\lambda$. Then time period will be given as
(Consider $k$ as Coulomb's constant)
$\mathrm{T}^2=\frac{4 \pi^2 \mathrm{~m}}{2 \mathrm{k} \lambda \mathrm{q}} \mathrm{r}^3$
$T=2 \pi r \sqrt{\frac{m}{2 k \lambda q}}$
$\mathrm{T}=\frac{1}{2 \pi \mathrm{r}} \sqrt{\frac{\mathrm{m}}{2 \mathrm{k} \lambda \mathrm{q}}}$
$\mathrm{T}=\frac{1}{2 \pi} \sqrt{\frac{2 \mathrm{k} \lambda \mathrm{q}}{\mathrm{m}}}$
Electric charges of $1\,\mu C,\, - 1\,\mu C$ and $2\,\mu C$ are placed in air at the corners $A$, $B$ and $C$ respectively of an equilateral triangle $ABC$ having length of each side $10 \,cm$. The resultant force on the charge at $C$ is......$N$
Three points charges are placed at the corners of an equilateral triangle of side $L$ as shown in the figure.
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 : $\frac{1}{{\left( {4\pi {\varepsilon _0}} \right)}} = 9 \times {10^9}\,Nm/{C^2}$)
Write expression of Coulombian force acting between two charges kept in medium.