Ten positively charged particles are kept fixed on the $x-$axis at points $x=10 \mathrm{cm}, 20 \mathrm{cm}, 30 \mathrm{cm}, \dots , 100 \mathrm{cm}.$The charge of the first particle is $1.0\times {10}^{-8} \mathrm{C},$the second particle is $8\times {10}^{-8} \mathrm{C},$the third particle is $27\times {10}^{-8} \mathrm{C}$and so on. The tenth particle has a charge $1000\times {10}^{-8} \mathrm{C}.$Find the magnitude of the electric force acting on a $1 \mathrm{C}$charge placed at the origin.

In the given figure, two tiny conducting balls of identical mass $m$and identical charge $q$hang from non-conducting threads of equal length $L.$Assume that $\text{θ}$is so small that $\tan \text{θ}\approx \sin \text{θ},$then for equilibrium $x$is equal to

Three charges $q_1, q_2$and $q_3$are placed as shown in the figure. The magnitude of $q_1$is $2 \mathrm{\mu C}\text{, }$but its sign and the value of the charge $q_2$are not known. The charge $q_3$is $+4 \mathrm{\mu C}$and the net force $\overrightarrow{\mathrm{F}}$on the charge $q_3$is in the negative $x-$direction. Select the incorrect option.

In the figure shown, $A$ is a fixed charge and $B$ (of mass $m$) is given a velocity $v$ perpendicular to line $AB.$ At this moment, the radius of curvature of the resultant path of $B$ is