Charges are placed on the vertices of a square as shown. Let $\vec E$ be the electric field and $V$ be the potential at the centre. If the charges on $A$ and $B$ are interchanged with those on $D$ and $C$ respectively,then

Two free point charges $+q$ and $+4q$ are a distance $R$ apart. $A$ third charge is so placed that the entire system is in equilibrium. Then the third charge is :-

Consider a uniformly charged hemispherical shell of radius $R$ and charge $Q$. If the electric field at point $A (0, 0, -z_0)$ is $\vec E$,then find the electric field at point $B (0, 0, z_0)$,where $z_0 < R$.

Three identical charges are placed at the three corners of an equilateral triangle as shown in the figure. Which of the following statements is true for the electric field $E$ and electric potential $V$ at the center $O$?

Three parallel metal plates,each of area $A$,are placed as shown in the figure. Charges $Q_1$,$Q_2$,and $Q_3$ are given to them. Edge effects are negligible. Calculate the charge on the two outermost surfaces '$a$' and '$f$'.

Six point charges are placed at the vertices of a regular hexagon as shown in the figure. Three of the charges are $+q$ and the other three are $-q$. Starting from $P$ and moving clockwise,the electric field at the center $O$ is twice the electric field due to a single charge $+q$ at $R$. Which of the following arrangements of charges at $P, Q, R, S, T, U$ is correct?