A square loop of side $l$ having uniform linear charge density $\lambda$ is placed in the $x-y$ plane as shown in the figure. There is a non-uniform electric field $\overrightarrow{E}=\frac{a}{l}(x+l)\hat{i}$ where $a$ is a constant. Find the resultant electric force in $\mathrm{\mu N}$ on the loop if $l=10 \mathrm{cm}, a=2 \mathrm{N}/\mathrm{C}$ and charge density $\lambda =2 \mathrm{\mu C}/\mathrm{m}$.

Three identical positive point charges, as shown, are placed at the vertices of an isosceles right angled triangle. Which of the numbered vectors coincides in direction with the electric field at the mid-point $M$of the hypotenuse?

In the following four situations, the charged particles are at an equal distance from the origin. Arrange them according to the magnitude of the net electric field at origin (greatest first).

(i)

(ii)

(iii)

(iv)

Five point charges each having magnitude $q$ are placed at the corner of hexagon, as shown in the figure. Net electric field at the centre $O$ is $\overrightarrow{E}$. To get the net electric field at $O$ as $6\overrightarrow{E},$the charge placed on the remaining sixth corner should be

The following figures show regular hexagons, with charges at the vertices. In which of the following cases the electric field at the center is not zero?

Charges $q, 2q, 3q$and $4q$are placed at the corners $A, B, C$and $D$of a square $ABCD$as shown in the following figure. The direction of the electric field at the center of the square is along