Two point charges $+2 \ C$ and $+6 \ C$ separated by a distance '$r$' repel each other with a force of $18 \ N$. If a negative charge of $-4 \ C$ is added to each of these charges,then the force experienced by them is:

In one model of the electron,the electron of mass $m_e$ is thought to be a uniformly charged shell of radius $R$ and total charge $e$,whose electrostatic energy $E$ is equivalent to its mass $m_e$ via Einstein's mass-energy relation $E = m_e c^2$. In this model,$R$ is approximately ($m_e = 9.1 \times 10^{-31} \, kg$,$c = 3 \times 10^8 \, ms^{-1}$,$1 / 4 \pi \varepsilon_0 = 9 \times 10^9 \, Nm^2C^{-2}$,magnitude of the electron charge $e = 1.6 \times 10^{-19} \, C$).

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

$A$ charge $+Q$ is placed at each of the diagonally opposite corners of a square. $A$ charge $-q$ is placed at each of the other diagonally opposite corners as shown. If the net electrical force on $+Q$ is zero,then $\frac{+Q}{-q}$ is equal to

Two equally charged,identical metal spheres $A$ and $B$ repel each other with a force '$F$'. The spheres are kept fixed with a distance '$r$' between them. $A$ third identical,but uncharged sphere $C$ is brought in contact with $A$ and then placed at the mid-point of the line joining $A$ and $B$. The magnitude of the net electric force on $C$ is

Two charges $+q$ and $-3q$ are placed on the $x$-axis separated by a distance $d$. ($-3q$ is to the right of $q$). Where should a third charge $2q$ be placed such that it will not experience any net force?