A point charge $+q$ is placed at the centre of a cube of side $L$. The electric flux emerging from the cube is
- $\frac{q}{\varepsilon_{0}}$
- Zero
- $\frac{6qL^{2}}{\varepsilon_{0}}$
- $\frac{q}{6L^{2}\varepsilon_{0}}$
The Correct Option is A
Solution and Explanation
Top Questions on Gauss Law
- 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 __________ \( \text{N m}^2/\text{C} \).
- JEE Main - 2024
- Physics
- Gauss Law
- A charge q is placed at the center of one of the surface of a cube. The flux linked with the cube is :-
- JEE Main - 2024
- Physics
- Gauss Law
- There are two cubical Gaussian surface carrying charges as shown. Find ratio of fluxes through surface \(C_1\) and \(C_2\):
- JEE Main - 2024
- Physics
- Gauss Law
- A cubical Gaussian surface has side of length a = 10 cm. Electric field lines are parallel to x-axis as shown. The magnitudes of electric fields through surfaces ABCD and EFGH are 6kNC-1 and 9kNC-1 respectively. Then the total charge enclosed by the cube is
[Take ε0 = 9 × 10-12 Fm-1]
- KCET - 2023
- Physics
- Gauss Law
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 $\vec{E}=E_0 x \hat{ t }$ Where $E_0=4 \times 10^4 NC ^{-1} m ^{-1}$ If $a=2 cm$, the charge contained in the cubical volume is $Q \times 10^{-14} C$ The value of $Q$ is ___ Take \(E_{0}=9\times 10^{-2}C^{2}/Nm^{2}\)
- JEE Main - 2023
- Physics
- Gauss Law
Questions Asked in BITSAT exam
- Minimum value of 5cos(2x) + 5sin(2x)
- BITSAT - 2023
- Trigonometric Functions
- Two capacitors, of capacitance C, are connected in series. If one of them is filled with a dielectric substance K, what is the effective capacitance?
- BITSAT - 2023
- electrostatic potential and capacitance
- What is the dimension of the Gravitational constant?
- BITSAT - 2023
- Gravitation
NaOH is deliquescent
- BITSAT - 2023
- States of matter
- The freezing point of the 0.05 molal solution of non - electrolyte in water is? (kf = 1.86)
- BITSAT - 2023
- Solutions
Concepts Used:
Gauss Law
Gauss law states that the total amount of electric flux passing through any closed surface is directly proportional to the enclosed electric charge.
Gauss Law:
According to the Gauss law, the total flux linked with a closed surface is 1/ε0 times the charge enclosed by the closed surface.
For example, a point charge q is placed inside a cube of edge ‘a’. Now as per Gauss law, the flux through each face of the cube is q/6ε0.
Gauss Law Formula:
As per the Gauss theorem, the total charge enclosed in a closed surface is proportional to the total flux enclosed by the surface. Therefore, if ϕ is total flux and ϵ0 is electric constant, the total electric charge Q enclosed by the surface is;
Q = ϕ ϵ0
The Gauss law formula is expressed by;
ϕ = Q/ϵ0
Where,
Q = total charge within the given surface,
ε0 = the electric constant.