Electric flux through a surface of area $100$ $m^2$ lying in the $xy$ plane is (in $V-m$) if $\vec E = \hat i + \sqrt 2 \hat j + \sqrt 3 \hat k$

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

The magnitude of the average electric field normally present in the atmosphere just above the surface of the Earth is about $150\, N/C$, directed inward towards the center of the Earth . This gives the total net surface charge carried by the Earth to be......$kC$ [Given ${\varepsilon _0} = 8.85 \times {10^{ - 12}}\,{C^2}/N - {m^2},{R_E} = 6.37 \times {10^6}\,m$]

A long cylindrical shell carries positive surface charge $\sigma$ in the upper half and negative surface charge $-\sigma$ in the lower half. The electric field lines around the cylinder will look like figure given in : (figures are schematic and not drawn to scale)

Is electric flux scalar or vector ?

A uniformly charged conducting sphere of $2.4\; m$ diameter has a surface charge density of $80.0\; \mu \,C/m^2$.

$(a)$ Find the charge on the sphere.

$(b)$ What is the total electric flux leaving the surface of the sphere?