List of top Physics Questions on Gauss Law asked in JEE Main

There are two cubical Gaussian surface carrying charges as shown. Find ratio of fluxes through surface \(C_1\) and \(C_2\):
There are two cubical Gaussian surface carrying charges as shown
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 :
electric potential at the center of two concentric half rings

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 ILIST II
AGauss's Law in ElectrostaticsI\(\oint \vec{E} \cdot d \vec{l}=-\frac{d \phi_B}{d t}\)
BFaraday's LawII\(\oint \vec{B} \cdot d \vec{A}=0\)
CGauss's Law in MagnetismIII\(\oint \vec{B} \cdot d \vec{l}=\mu_0 i_c+\mu_0 \in_0 \frac{d \phi_E}{d t}\)
DAmpere-Maxwell LawIV\(\oint \vec{E} \cdot d \vec{s}=\frac{q}{\epsilon_0}\)
Choose the correct answer from the options given below: