$A$ ring of radius $R$ has charge $-Q$ distributed uniformly over it. The charge that should be placed at the center of the ring such that the electric field becomes zero at a point on the axis of the ring at a distance $R$ from the center of the ring will be:

Four point charges are placed at the vertices of a regular hexagon as shown in the figure below. What will be the net electric field at the centre?

$A$ semicircular ring of radius $0.5 \ m$ is uniformly charged with a total charge of $1.4 \times 10^{-9} \ C$. The electric field intensity at the center of the ring is ........ $V/m$.

The three charges $q/2, q$ and $q/2$ are placed at the corners $A, B$ and $C$ of a square of side '$a$' as shown in the figure. The magnitude of the electric field $(E)$ at the corner $D$ of the square is:

$A$ circular wire loop of radius $10 \ cm$ carries a total charge of $10^{-5} \ C$ distributed uniformly over its length. $A$ small length of $3.14 \times 10^{-6} \ m$ of wire is cut off. The magnitude of the electric field at the centre due to the remaining wire is:
(Assume $\frac{1}{4 \pi \epsilon_{0}} = 9 \times 10^{9} \ SI$ units) (in $N \ C^{-1}$)

An electric field is given by $\vec{E} = e_1 \hat{i} + e_2 \hat{j} + e_3 \hat{k}$. $A$ charge $Q$ is moved by a displacement vector $\vec{r} = a \hat{i} + b \hat{j}$. The work done is: