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 $g = 10 \, ms^{-2}$]

Electrostatic force between two identical charges placed in vacuum at a distance of $r$ is $F$. $A$ slab of width $\frac{r}{5}$ and dielectric constant $9$ is inserted between these two charges. The new force between the charges is:

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

Two identical conducting spheres carrying different charges attract each other with a force $F$ when placed in air at a distance $d$ apart. The spheres are brought into contact and then returned to their original positions. Now,the two spheres repel each other with a force whose magnitude is equal to the initial attractive force. The ratio between the initial charges on the spheres is:

Two point charges $q_1$ and $q_2$ are placed at a distance of $50 \ cm$ from each other in air and interact with a certain force. Now,these charges are placed in an oil with a relative permittivity of $5$. If the force between them remains the same,the distance between them in the oil is ........ $cm$.

Two identical simple pendulums each of length $L = 5 \, cm$ are suspended from the same support. When the bobs are given an equal charge of $q = 2 \, \mu C$ each, the distance between the bobs becomes $d = 6 \, cm$. Find the mass $m$ of each bob. (Take $g = 10 \, m/s^2$ and $k = 9 \times 10^9 \, N \cdot m^2/C^2$). (in $ \, kg$)