Three charges $Q,+q$ and $+q$ are placed at the vertices of a right angled isosceles triangle as shown in figure. The net electrostatics energy of the configuration is zero if $Q$ is equal to

Two charges $q_1$ and $q_2$ are placed $30 \mathrm{cm}$ apart, as shown in figure. A third charge $q_3$ is moved along the arc of a circle of radius $40 \mathrm{cm}$ from $C$ to $D$. The change in the potential energy of the system is $\frac{q_3}{4{\mathrm{\pi \epsilon }}_0}k,$ where $k$ is

If linear charge density of a bent wire as shown in the figure is $\mathrm{\lambda }$. Then.

A ring of radius $R$ is placed at a distance $R$ from a point charge $q$ as shown in figure. Total electric flux passing through the ring would be

A point charge $q$ is placed at a distance $r$ from the centre $O$ of an uncharged spherical shell of inner radius $R$ and outer radius $2R.$ The distance is $r<R.$ The electric potential at the centre of the shell will be

A hollow sphere of radius $r$ is put inside another hollow sphere of radius $R$. The charges on the two are $+Q$ and $-q$ as shown in the figure. A point $P$ is located at a distance $x$ from the common centre such that $r<x<R$. The potential at the point $P$ is