Two small metal spheres $A$ and $B$ charged positively are separated by $2 \mathrm{m}$ in air. The force on a charge of $+1 \mathrm{C}$ placed on the line joining the centres of the spheres and at a distance of $0.5 \mathrm{m}$ from $A$ is found to be zero. The ratio $q_A:q_B$ of charges on $A$ and $B$ is

Two equal point charges of $1 \mu \mathrm{C}$ each are located at points $(\hat{\mathrm{i}}+\hat{\mathrm{j}}+\hat{\mathrm{k}}) \mathrm{m}$ and $(2\hat{\mathrm{i}}+3\hat{\mathrm{j}}-\hat{\mathrm{k}}) \mathrm{m}$. What is the magnitude of electrostatic force between them?

Two small spheres with mass $m_1$ and $m_2$ hang from massless insulating threads of length $l_1$ and $l_2.$ The two spheres carry charges $q_1$ and $q_2$, respectively. The spheres are hung such that they are on the same horizontal level and the threads are inclined to the vertical at angles ${\theta }_1$ and ${\theta }_2.$ Which of the condition is required if ${\theta }_1={\theta }_2?$

Four point charges of $+3\mathrm{\mu C},+2\mathrm{\mu C},+3\mathrm{\mu C}$ and $+2\mathrm{\mu C}$ are placed at the corners of a rectangle $A, B, C$ and $D$. The electrical force will be least between the charges