Two charges 2 $\mathrm{\mu C}$ and 8 $\mathrm{\mu C}$ are separated by 6 cm. The neutral point is at:

1.	4 cm from 2  μC.
2.	2 cm from 2  μC .
3.	2 cm from 8  μC .
4.	3 cm from 8  μC .

The ratio of the electric flux linked with shell \(A\) and shell \(B\) in the diagram shown below is:

An electric dipole is kept at the origin as shown in the diagram. The point A, B, C are on a circular arc with the centre of curvature at the origin. If the electric fields at A, B and C respectively are $\overrightarrow{E_1},$ $\overrightarrow{E_2},$ $\overrightarrow{E_3}$ , then which of the following is incorrect? \(\left ( d\gg l \right )\)

                
1.  $\overrightarrow{E_1}$ $=$ $-\overrightarrow{E_3}$
2.  $\overrightarrow{E_1}$ $=$ $-2\overrightarrow{E_2}$
3.  $\overrightarrow{E_1}$ $=$ $\overrightarrow{E_3}$
4.  $\overrightarrow{E_3}$ $=$ $-\overrightarrow{2E_2}$

An electric dipole is placed at the centre of a sphere. Which of the following statements is correct?

A charged particle q of mass m is released on the y-axis at y = a in an electric field $\overrightarrow{E}=-4y\hat{j}$. The speed of particle on reaching the origin will be:

1.  $\sqrt{\frac{2a}{mq}}$

2.  $\frac{a}{\sqrt{mq}}$

3.  $2a\sqrt{\frac{q}{m}}$

4.  $2\sqrt{\frac{a}{mq}}$

A point charge q is placed at the center of the open face of a hemispherical surface as shown in the figure. The flux linked with the surface is:

1.  zero

2.  $\frac{q}{2{\epsilon }_0}$

3.  $\frac{q}{{\epsilon }_0}$

4.  $q\pi r^2$

Four charges are arranged at the corners of a square ABCD as shown in the figure. The force on a positive charge kept at the center of the square is:

The net dipole moment of the system is of the magnitude:
         

1.  q $\times$ 2a

2.  2q $\times$ 2a

3.  q $\times$ a

4.  2 $\times$ (2q $\times$ 2a)

Two-point charges, +q and –q are held fixed at (–d, 0) and (d, 0) respectively of an (x, y) coordinate system. Then: 

The charge on 500 cc of water due to protons will be: