The three point charges shown in the figure lie along a straight line. The energy needed to exchange the position of the central positive charge with one of the negative charges is,

 

 

Three charges $+q, -q$ and $+2q$are placed at the vertices of a right-angled triangle (isosceles triangle) as shown below. The net electrostatic energy of the configuration is,

Three equal charges $Q$ are placed at the three vertices of an equilateral triangle. What should be the value of a charge that when placed at the centroid reduces the interaction energy of the system to zero?

A spherical balloon of radius $R$ is charged uniformly on its surface with surface density $\sigma$. Find the work done against electric forces in expanding it upto radius $2R$.

Three point charges $q, 2q$ and $8q$ are to be placed on a $9 \mathrm{cm}$ long straight line. Find the positions where the charges should be placed such that the potential energy of this system is minimum.

A charged particle $q$ is shot towards another charged particle $Q,$ which is fixed, with speed $v$. It approaches $Q$ up to a closest distance $r$ and then returns. If $q$ was given a speed $2v,$ the closest distance of approach would be,

A dipole of dipole moment $p$ is placed at the centre of a non-conducting spherical shell of radius $r$. If the shell is uniformly charged by a surface charge density $\mathrm{\sigma }$, then the interaction energy between the dipole and the shell is,

A dipole of dipole moment $\overrightarrow{p}=(2\hat{\mathrm{i}}-3\hat{\mathrm{j}}+4\hat{\mathrm{k}}) \mathrm{cm}$ is kept at a point $A$ whose coordinates are $(1,-1,3)$. If an external electric field $\overrightarrow{E}=(5\hat{\mathrm{i}}+2\hat{\mathrm{j}}-3\hat{\mathrm{k}}) \mathrm{V} {\mathrm{m}}^{-1}$ is applied then the potential energy of the dipole be,

An electric field $E$, whose direction is radially outwards varies with distance from origin $r$ as shown in the graph. $E$ is taken as positive if its direction is away from the origin. The work done by electric field on a $2 \mathrm{C}$ charge if it is taken from $(1,1,0)$to $(3,0,0)$ is,