A charge $q$ is placed in the middle of a line joining the two equal and like point charge $Q$. This charge $q$ will remain in equilibrium for which value of $q$ is

A thin metallic wire having cross sectional area of $10^{-4} \mathrm{~m}^2$ is used to make a ring of radius $30 \mathrm{~cm}$. A positive charge of $2 \pi \mathrm{C}$ is uniformly distributed over the ring, while another positive charge of $30$ $\mathrm{pC}$ is kept at the centre of the ring. The tension in the ring is__________ $\mathrm{N}$; provided that the ring does not get deformed (neglect the influence of gravity). (given, $\frac{1}{4 \pi \epsilon_0}=9 \times 10^9 \mathrm{SI}$ units)

The magnitude of electric force on $2\, \mu \,C$ charge placed at the centre $O$ of two  equilateral triangles each of side $10 \,cm$, as shown in figure is $P$. If charge $A, B, C, D, E$ and $F$ are $2\, \mu \,C, 2\, \mu \,C, 2\, \mu \,C,-2\, \mu \,C, -2\, \mu \,C, -2\, \mu \,C$   respectively, then $P$ is :.....$N$

Two insulated charged copper spheres $A$ and $B$ have their centres separated by a distance of $50 \;cm$.  the charge on each is $6.5 \times 10^{-7}\; C?$ Suppose the spheres $A$ and $B$ have identical sizes.A third sphere of the same size but uncharged is brought in contact with the first, then brought in contact with the second, and finally removed from both. What is the new force of repulsion between $A$ and $B?$

Four point charges $q_{A}=2\; \mu C, q_{B}=-5\; \mu C,$ $q_{C}=2\; \mu C,$ and $q_{D}=-5\;\mu C$ are located at the corners of a square $ABCD$ of side $10\; cm .$ What is the force on a charge of $1 \;\mu C$ placed at the centre of the square?

Two identical balls having like charges and placed at a certain distance apart repel each other with a certain force. They are brought in contact and then moved apart to a distance equal to half their initial separation. The force of repulsion between them increases $4.5$ times in comparison with the initial value. The ratio of the initial charges of the balls is