When a positive charge inside a metallic shell of thickness t is moved, then induced surface charge density

1 On inner surface will same and on the outer surface will change

2 On inner surface will change and on the outer surface will same

3 On the inner and outer surface will the same

4 On the inner and outer surface will change

Charge distribution at three vertices of an equilateral of side is shown in the figure. The net electric dipole moment of the system is

1.  $2\sqrt{3}qa\hat{j}$

2.  $-2\sqrt{3}qa\hat{j}$

3.  $2\sqrt{3}qa\hat{j}+2\sqrt{3}qa\hat{j}$

4.  $-2\sqrt{3}qa\hat{j}-2\sqrt{3}qa\hat{j}$

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: