Two identical spheres,each of mass $1 \, g$,carry an identical charge of $10^{-9} \, C$. They are suspended by strings of equal length. If the distance between the centers of the spheres is $0.3 \, cm$,what is the angle made by the string with the vertical?

Two small spheres,each having an equal positive charge $Q$ (Coulomb),are suspended by two insulating strings of equal length $L$ (metre) from a rigid hook. The whole setup is taken into a satellite where there is no gravity. The two balls are now held by electrostatic forces in a horizontal position. The tension in each string is then:

Two identical pendulums $A$ and $B$ are suspended from the same point. The bobs are given positive charges,with $A$ having more charge than $B$. They diverge and reach equilibrium,with $A$ and $B$ making angles $\theta_1$ and $\theta_2$ with the vertical,respectively. Then:

Explain the vector form of Coulomb's law and its importance. Write some important points regarding the vector form of Coulomb's law.

Two beads,each with charge $q$ and mass $m$,are on a horizontal,frictionless,non-conducting,circular hoop of radius $R$. One of the beads is glued to the hoop at some point,while the other one performs small oscillations about its equilibrium position along the hoop. The square of the angular frequency of the small oscillations is given by [ $\varepsilon_0$ is the permittivity of free space.]

Two identical charges repel each other with a force equal to $10 \text{ mg}$ wt when they are $0.6 \text{ m}$ apart in air $(g = 10 \text{ ms}^{-2})$. The value of each charge is: