Six point charges are placed at the vertices of a regular hexagon of side $a$ as shown. If $E$ represents the electric field and $V$ represents the electric potential at the center $O$,then:

The charge per unit length of the four quadrants of the ring are $2\lambda$,$-2\lambda$,$\lambda$,and $-\lambda$ respectively. The electric field at the centre is

The figure shows a nonconducting ring which has positive and negative charge non-uniformly distributed on it such that the total charge is zero. Which of the following statements is true?

Two equal charges $q$ are placed at a distance of $2a$ on the $x$-axis. A third charge $q$ of mass $m$ is placed at the midpoint between them. If this charge is displaced by a small distance $x$ from the equilibrium position, the particle will:

Two identical charged spheres are suspended by strings of equal lengths. The strings make an angle of $30^{\circ}$ with each other. When suspended in a liquid of density $0.8 \; g \, cm^{-3}$,the angle remains the same. If the density of the material of the sphere is $1.6 \; g \, cm^{-3}$,the dielectric constant of the liquid is:

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