$A$ charge $q$ is placed at the centre of the line joining two equal charges $Q$. The system of the three charges will be in equilibrium if $q$ is equal to:

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 $\frac{1}{4 \pi \varepsilon_{0}} = 9 \times 10^{9} \; Nm^{2} C^{-2}$)

According to Coulomb's Law,which is the correct relation for the following diagram?

Two small spheres each of mass $10 \, mg$ are suspended from a point by threads $0.5 \, m$ long. They are equally charged and repel each other to a distance of $0.20 \, m$. The charge on each of the sphere is $\frac{a}{21} \times 10^{-8} \, C$. The value of $a$ will be ...... . [Given $g = 10 \, ms^{-2}$]

Three charges $q, Q$ and $+4q$ are placed in a straight line of length $d$ at points at distances $0, \frac{d}{2}$ and $d$ respectively. In order to make the net force on $q$ to be zero,the value of $Q$ should be

The value of electric permittivity of free space is