A charge $Q$ is divided into two parts of $q$ and $Q - q$. If the coulomb repulsion between them when they are separated is to be maximum, the ratio of $\frac{Q}{q}$ should be

A capacitor $C = 100$ $ \mu F$ is connected to three resistors each of resistance $1$ $kW$ and a battery of emf $9$ $V$. The switch $S $ has been closed for long time so as to charge the capacitor. When switch $S $ is opened, the capacitor discharges with time constant.....$ms$ 

The adjoining diagram shows the electric lines of force emerging from a charged body. If the electric fields at $A$ and $B$ are $E_A$ and $E_B$ respectively and the distance between them is $r$, then

A parallel plate capacitor has circular plates of $10\, cm$ radius separated by an air-gap of $1\, mm$ . It is charged by connecting the plates to a $100\, volt$ battery. Then the change in energy stored in the capacitor when the plates are moved to a distance of $1\, cm$ and the plates are maintained in connection with the battery, is

The electric potential $V$ at any point $(x,y,z)$ in space is given by equation $V = 4x^2\,volt$ where $x, y$ and $z$ are all in metre. The electric field at the point $(1\,m, 0, 2\,m)$ in $V/m$ is

A hollow metal sphere of radius $5\,cm$ is charged such that the potential on its surface is $10\,V$. The potential at a distance of $2\,cm$ from the centre of the sphere.......$V$