As shown in the figure,charges $+q$ and $-q$ are placed at the vertices $B$ and $C$ of an isosceles triangle. The potential at the vertex $A$ is

Three identical charges of $10 \ \mu C$ are placed at the vertices of an equilateral triangle of side $10 \ cm$. The electrostatic potential energy of the system is ....... $J$.

$(a)$ Calculate the potential at a point $P$ due to a charge of $4 \times 10^{-7} \; C$ located $9 \; cm$ away.
$(b)$ Hence,obtain the work done in bringing a charge of $2 \times 10^{-9} \; C$ from infinity to the point $P$. Does the answer depend on the path along which the charge is brought?

$A$ point charge $-q$ is carried from a point $A$ to another point $B$ on the axis of a charged ring of radius $r$ carrying a charge $+q$. If the point $A$ is at a distance $\frac{4}{3} r$ from the centre of the ring and the point $B$ is $\frac{3}{4} r$ from the centre but on the opposite side,what is the net work that needs to be done for this?

$A$ spherical charged conductor has surface charge density $\sigma$. The electric field on its surface is $E$ and the electric potential of the conductor is $V$. Now,the radius of the sphere is halved while keeping the charge constant. The new values of the electric field and potential would be:

If a $10 \mu C$ charge exists at the centre of a square,the work done in moving a $2 \mu C$ point charge from corner $A$ to corner $B$ of a square $ABCD$ is