Q 1 :    

An electric field is given by $(6\hat{i}+5\hat{j}+3\hat{k})N/C.$ The electric flux through a surface area $30\hat{i}$ $m^2$  lying in YZ-plane (in SI unit) is              [2024]

• 180

   

• 90

   

• 150

   

• 60

   

Q 2 :    

Three infinitely long charged thin sheets are placed as shown in figure. The magnitude of electric field at the point P is $\frac{x\sigma }{{\epsilon }_0}$. The value of $x$ is _____ (all quantities are measured in Sl units).              [2024]

Q 3 :    

A charge q is placed at the center of one of the surfaces of a cube. The flux linked with the cube is          [2024]

• $\frac{q}{2{\epsilon }_0}$

   

• $\frac{q}{4{\epsilon }_0}$

   

• $\frac{q}{8{\epsilon }_0}$

   

• $\text{zero}$

   

Q 4 :    

Five charges +q, +5q, −2q, +3q and −4q are situated as shown in the figure. The electric flux due to this configuration through the surface S is        [2024]

• $\frac{5q}{{\epsilon }_0}$

   

• $\frac{4q}{{\epsilon }_0}$

   

• $\frac{3q}{{\epsilon }_0}$

   

• $\frac{q}{{\epsilon }_0}$

   

Q 5 :    

Two charges of 5Q and −2Q are situated at the points (3a,0) and (−5a,0) respectively. The electric flux through a sphere of radius 4a having center at origin is      [2024]

• $\frac{2Q}{{\epsilon }_0}$

   

• $\frac{5Q}{{\epsilon }_0}$

   

• $\frac{7Q}{{\epsilon }_0}$

   

• $\frac{3Q}{{\epsilon }_0}$

   

Q 6 :    

$C_1$ and $C_2$ are two hollow concentric cubes enclosing charges 2Q and 3Q respectively as shown in the figure. The ratio of electric flux passing through $C_1$ and $C_2$ is    [2024]

• 2 : 5

   

• 5 : 2

   

• 2 : 3

   

• 3 : 2

   

Q 7 :    

An infinite plane sheet of charge having uniform surface charge density $+{\sigma }_s$ $C/m^2$ is placed on the $x-y$ plane. Another infinitely long line charge having uniform linear charge density $+{\lambda }_e$$C/m$ is placed at $z=4$ m plane and parallel to the y-axis. If the magnitude values $\mid {\sigma }_s\mid =2\mid {\lambda }_e\mid$then at point $(0,0,2),$ the ratio of magnitudes of electric field values due to sheet charge to that of line charge is $\pi \sqrt{n}:1$. The value of $n$ is ______ .       [2024]

Q 8 :    

An electric field, $\overrightarrow{E}=\frac{2\hat{i}+6\hat{j}+8\hat{k}}{\sqrt{6}}$ passes through the surface of $4m^2$ area having unit vector $\hat{n}=\left(\frac{{\displaystyle 2\hat{i}+\hat{j}+\hat{k}}}{{\displaystyle \sqrt{6}}}\right).$ The electric flux for that surface is ____ Vm.   [2024]

Q 9 :    

An electric field $\overrightarrow{E}=\left(2x\hat{i}\right)N{C}^{-1}$ exists in space. A cube of side 2 m is placed in the space as per figure given below. The electric flux through the cube is _____ ${\text{Nm}}^2/\text{C}.$  [2024]