Idea of Symmetry

Q.

A cube of side \( l \) is placed in a uniform field \( E \), where \( E=E \hat{i} \). The net electric flux through the cube is

Q.

A cylinder of radius R and length L is placed in a uniform electric field E parallel to the cylinder axis. The total flux for the surface of the cylinder is given by

1. Zero

2. 
   

3. 
   

4. 
   

Q.

It is not convenient to use a spherical Gaussian surface to find the electric field due to an electric dipole using Gauss's theorem because

1. Gauss's law fails in this case

2. This problem does not have spherical symmetry

3. Coulomb's law is more fundamental than Gauss's law

4. Spherical Gaussian surface will alter the dipole moment

Q.

A point charge \( q \) is placed at a distance \( a / 2 \) directly above the centre of a square of side \( a \). The electric flux through the square is

Q.

Which Gaussian surface would you prefer to choose if you had to calculate electric field due to a charge distribution such that the integration complexity is reduced?

1. the one which is a sphere around the charged distribution

2. The one where electric field and area vector has constant angle and electric field magnitude has constant value

3. the one which has the same direction for area vectors of all infinitesimal elements

4. the one that has a the same direction of electric field at all infinitesimal elements

Q.

Eight dipoles of charges of magnitude \( e \) are placed inside a cube. The total electric flux coming out of the cube will be

Q. A cubical region of side a has its centre at the origin. It encloses three fixed point charges, -q at (0, $-\frac{a}{4}$, 0), +3q at (0, 0, 0) and -q at (0, $+\frac{a}{4}$, 0). Choose the correct option(s).

1. The net electric flux crossing the plane x = $+\frac{a}{2}$ is equal to the net electric flux crossing the plane x = $-\frac{a}{2}$.
2. The net electric flux crossing the plane y = $+\frac{a}{2}$ is more than the net electric flux crossing the plane y = $-\frac{a}{2}$.
3. The net electric flux crossing the entire region is $\frac{q}{{\epsilon }_0}$.
4. The net electric flux crossing the plane z = $+\frac{a}{2}$ is equal to the net electric flux crossing the plane x = $+\frac{a}{2}$.

Q. A point charge is placed at points P1, P2 and P3. Find the flux through the hemispherical surface.
Using Symmetry

1. $0,\frac{q}{{ϵ}_0},\frac{q}{2{ϵ}_0}$
   
2. $0,\frac{2q}{{ϵ}_0},\frac{q}{2{ϵ}_0}$
3. $0,\frac{q}{{ϵ}_0},\frac{q}{{ϵ}_0}$
4. $0,\frac{2q}{{ϵ}_0},\frac{q}{{ϵ}_0}$

Q. A cube of side $a$ is placed such that the nearest face which is parallel to the y-z plane, is at a distance $a$ from the origin. The electric field components are $E_x=\beta x^{1/2},E_y=E_z=0$.
The charge within the cube is

1. $\sqrt{2}\beta {ϵ}_a{a}^{5/2}C$
2. $(\sqrt{2}-1)\beta {ϵ}_o{a}^{5/2}C$
3. $-\beta {ϵ}_o{a}^{5/2}C$
4. zero

Q.

A square plate of side 'a' is kept below an infinite line charge of charge per unit length $\lambda$ (as shown in figure). Electric flux associated with the plate is $\frac{3\lambda a}{n\pi {ϵ}_o}ta{n}^{-1}\left(\frac{1}{2}\right).$
Here, n is