$A$ proton and an anti-proton come close to each other in vacuum such that the distance between them is $10 \, cm$. Consider the potential energy to be zero at infinity. The velocity at this distance will be ........... $\, m/s$.

Two charges placed in air repel each other with a force of $10^{-4} \ N$. When oil is introduced between the charges, the force becomes $2.5 \times 10^{-5} \ N$. The dielectric constant of the oil is:

When the distance between the charged particles is halved,the force between them becomes

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

Two identical spheres,each carrying a charge $Q = 10 \ \mu C$,are suspended from a single rigid support by strings of length $L = 1 \ m$. In the equilibrium position,if the angle between the two strings is $60^\circ$,what is the tension $T$ in the strings (in $N$)? (Given: $\frac{1}{4\pi \varepsilon_0} = 9 \times 10^9 \ N \cdot m^2/C^2$)

The acceleration of an electron due to the mutual attraction between the electron and a proton when they are $1.6 \; \mathring{A}$ apart is,$(m_{e} \simeq 9 \times 10^{-31} \; kg, e = 1.6 \times 10^{-19} \; C)$. (Take $\frac{1}{4 \pi \varepsilon_{0}} = 9 \times 10^{9} \; Nm^{2} C^{-2}$)