List of top Physics Questions on Gauss Law

If the net flux through a cube is 1.05 N m$^2$ C$^{-1}$, what will be the total charge inside the cube? (Given: The permittivity of free space is $8.85 \times 10^{-12}$ C$^2$ N$^{-1}$ m$^{-2}$).

There are two cubical Gaussian surface carrying charges as shown. Find ratio of fluxes through surface $C_1$ and $C_2$:

A charge q is placed at the center of one of the surface of a cube. The flux linked with the cube is :-

An electric field $ \vec{E} = (2x \hat{i}) \, \text{N C}^{-1} $ exists in space. A cube of side $ 2 \, \text{m} $ is placed in the space as per the figure given below. The electric flux through the cube is __________ $ \text{N m}^2/\text{C} $.

The electric potential at the center of two concentric half rings of radii $R_1$ and $R_2$, having same linear charge density $\lambda$ is :

A cubical volume is bounded by the surfaces $ x = 0 $, $ x = a $, $ y = 0 $, $ y = a $, $ z = 0 $, $ z = a $. The electric field in the region is given by: \[ \vec{E} = E_0 x \hat{i} \]
Where $ E_0 = 4 \times 10^4 \, \text{NC}^{-1} \, \text{m}^{-1} $. If $ a = 2 \, \text{cm} $, the charge contained in the cubical volume is $ Q \times 10^{-14} \, \text{C} $. The value of $ Q $ is ______. (Take $ \epsilon_0 = 9 \times 10^{-12} \, \text{C}^2/\text{Nm}^2 $)

Match List I with List II

LIST I		LIST II
A	Gauss's Law in Electrostatics	I	$\oint \vec{E} \cdot d \vec{l}=-\frac{d \phi_B}{d t}$
B	Faraday's Law	II	$\oint \vec{B} \cdot d \vec{A}=0$
C	Gauss's Law in Magnetism	III	$\oint \vec{B} \cdot d \vec{l}=\mu_0 i_c+\mu_0 \in_0 \frac{d \phi_E}{d t}$
D	Ampere-Maxwell Law	IV	$\oint \vec{E} \cdot d \vec{s}=\frac{q}{\epsilon_0}$

Choose the correct answer from the options given below:

A disk of radius a/4 having a uniformly distributed charge -6C is placed in the x-y plane with its centre at (-a/2,0,0). A rod of length a carrying a uniformly distributed charge 8C is placed on the x-axis from x = a/4 to x = 5a/4. Two point charges -7C and 3C are placed at (-a/4,0,0) and (-3a/4,3a/4,0), respectively. Consider a cubical surface formed by six surfaces x=± a/2, y=± a/2, z=± a/2. The electric flux through this cubical surface is

A disk of radius $a/4$ having a uniformly distributed charge $6\,\text{C}$ is placed in the x-y plane with its centre at $(-a/2, 0, 0)$. A rod of length $a$ carrying a uniformly distributed charge $8\,\text{C}$ is placed on the x-axis from $x = a/4$ to $x = 5a/4$. Two point charges $-7\,\text{C}$ and $3\,\text{C}$ are placed at $(a/4, -a/4, 0)$ and $(-3a/4, 3a/4, 0)$ respectively. Consider a cubical surface formed by six surfaces $x = \pm a/2$, $y = \pm a/2$, $z = \pm a/2$. The electric flux through this cubical surface is

In a region of space having a uniform electric field $ E $, a hemispherical bowl of radius $ r $ is placed. The electric flux $ \Phi $ through the bowl is:

A charge +q is at a distance L/2 above a square of side L. Then what is the flux linked with the surface?