A circular plate subtends a solid angle $\mathrm{\pi }$ steradian at a point where a point charge 2Q is kept. The total electric flux through the circular plate is

1$\frac{Q}{4{\epsilon }_0}$

2 $\frac{Q}{2{\epsilon }_0}$

3 $\frac{2Q}{3{\epsilon }_0}$

4 $\frac{2Q}{{\epsilon }_0}$

A uniform electric field of strength E exists in a region. An electron is projected in the region perpendicularly with speed v as shown in the diagram. electron exits at point B. The electric field in the region is given by 

1 $\overrightarrow{E}=\frac{2xm{v}^2}{e{y}^2}\hat{i}$

2 $\overrightarrow{E}=\frac{xm{v}^2}{e{y}^2}\hat{i}$

3 $\overrightarrow{E}=-\frac{xm{v}^2}{e{y}^2}\hat{i}$

4 $\overrightarrow{E}=-\frac{2xm{v}^2}{e{y}^2}\hat{i}$

A point charge is placed at the center of the spherical Gaussian surface. The electric flux through the surface is changed if the:

In a region, volume charge density varies with radial distance r as $p=\frac{K}{r}$ where K is positive constant. The electric field E Varies with the radial distance in the region as

1. $\mathrm{E}\propto \mathrm{r}$

2. $\mathrm{E}\propto \frac{1}{r^2}$

3. $\mathrm{E}\propto r^2$

4. $\mathrm{E}\propto {\mathrm{r}}^0$

Which of the following is incorrect about electrostatic force?

1 it is conservative

2 it is a central force

3 Electrostatic field line never intersect

4 it also depends on the mass content of the body

Two charges each equal to $nq(n^{-1}<\sqrt{3})$ are placed at the corners of an equilateral triangle of side a. The electric field at the third corner is $E_{3, }where \left(E_0=\frac{q}{4{\mathrm{\pi \epsilon }}_0{\mathrm{a}}^2}\right)$ is-

1 $E_3=E_0$

2 $E_3<E_0$

3 $E_3>E_0$

4 $E_3\ge E_0$

Given below are two statements: 

Given below are two statements: 

Given below are two statements: 

In the light of the above statements choose the correct answer from the options given below: