Two metal sphere of radius $R$ and $3R$ have same surface charge density $\sigma$. If they are brought in contact and then separated, the surface charge density on smaller and bigger sphere becomes $\sigma_1$ and $\sigma_2$, respectively. The ratio $\dfrac{\sigma_1}{\sigma_2}$ is.

Three charges $q$, $Q$ and $+4q$ are placed in a straight line of length $d$ at points at distance $0$, $\dfrac{d}{3}$, $\dfrac{2d}{3}$ respectively. In order to make the net force on $q$ be zero, the value of $Q$ should be

Following figure indicates the electric potential V as a function through 4 regions on x-axis. Which of the following is correct for the electric field E in these regions?

A parallel plate capacitor has plate area $40 \text{ cm}^2$ and plates separation $2$ mm. The space between the plates is filled with a dielectric medium of a thickness $1$ mm and dielectric constant $5$. The capacitance of the system is