Four positive point charges $+q$ are kept at the four corners of a square of side $l$. The net electric field at the midpoint of any one side of the square is (take $\frac{1}{4 \pi \epsilon_0}=k$ ).

In the given figure, find the distance from point $A$ where the electric field is zero (in $cm$).

Two infinitely long parallel wires have linear charge densities $\lambda_1$ and $\lambda_2$ respectively. They are placed at a distance $R$ apart. The force per unit length on the wires will be ......

Six charges are placed around a regular hexagon of side length $a$ as shown in the figure. Five of them have charge $q$,and the remaining one has charge $x$. The perpendicular from each charge to the nearest hexagon side passes through the center $O$ of the hexagon and is bisected by the side.
Which of the following statement$(s)$ is(are) correct in $SI$ units?
$(A)$ When $x=q$,the magnitude of the electric field at $O$ is zero.
$(B)$ When $x=-q$,the magnitude of the electric field at $O$ is $\frac{q}{6 \pi \epsilon_0 a^2}$.
$(C)$ When $x=2q$,the potential at $O$ is $\frac{7q}{4 \sqrt{3} \pi \epsilon_0 a}$.
$(D)$ When $x=-3q$,the potential at $O$ is $\frac{3q}{4 \sqrt{3} \pi \epsilon_0 a}$.

$A$ hollow conducting shell is charged with $500 \,\mu C$. If a force of $562.5 \,N$ is exerted on the charge, the electric field intensity on its surface is ...... $N/C$.

$A$ spherical conductor of radius $2 \text{ cm}$ is uniformly charged with $3 \text{ nC}$. What is the electric field at a distance of $3 \text{ cm}$ from the center of the sphere?