$A$ point charge '$Q$' is placed at the centre of the line joining two equal charges '$+q$' and '$+q$'. The value of '$Q$' when the system is in equilibrium is

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

Three point charges are placed at the corners of an equilateral triangle of side $L$ as shown in the figure.

$A$ charge $Q$ is placed at each of the opposite corners of a square. $A$ charge $q$ is placed at each of the other two corners. If the net electrical force on $Q$ is zero,then $\frac{Q}{q} = $ . . . . . .

Two tiny spheres carrying charges $1.5 \; \mu C$ and $2.5 \; \mu C$ are located $30 \; cm$ apart. Find the potential and electric field:
$(a)$ at the mid-point of the line joining the two charges,and
$(b)$ at a point $10 \; cm$ from this midpoint in a plane normal to the line and passing through the mid-point.

Two small spheres of each charge $q$,mass $m$ and material density $d$ are suspended from a fixed point with the help of inextensible light threads. When the spheres are in air,the angle between the threads is $90^{\circ}$. When the spheres are suspended in a liquid of density $\frac{2}{3} d$,the angle between the threads is $60^{\circ}$. The value of the dielectric constant of the liquid is