Find out the surface charge density at the intersection of point $x =3\, m$ plane and $x$ -axis, in the region of uniform line charge of $8\, nC / m$ lying along the $z$ -axis in free space.

A charge $Q$ is placed at a distance $a/2$ above the centre of the square surface of edge $a$ as shown in the figure. The electric flux through the square surface is

The electric flux passing through the cube for the given arrangement of charges placed at the corners of the cube (as shown in the figure) is 

Figure shows the electric field lines around three point charges $A, \,B$ and $C$.

$(a)$ Which charges are positive ?

$(b)$ Which charge has the largest magnitude ? Why ?

$(c)$ In which region or regions of the picture could the electric field be zero ? Justify your answer.

$(i)$ Near $A$          $(ii)$ Near $B$          $(iii)$ Near $C$    $(iv)$ Nowhere

Electric field in a region is uniform and is given by $\vec{E}=a \hat{i}+b \hat{j}+c \hat{k}$. Electric flux associated with a surface of area $\vec{A}=\pi R^2 \hat{i}$ is

Three positive charges of equal value $q$ are placed at the vertices of an equilateral triangle. The resulting lines of force should be sketched as in