The electric field calculated by Gauss's law is the field due to the charges which:

1.  lie inside the Gaussian surface

2.  lie outside the Gaussian surface

3.  lie on the surface of the Gaussian surface

4.  lie either inside, outside, or on the Gaussian surface

A small sphere of mass m and having charge q is suspended by a silk thread of length l in a uniform horizontal electric field. If it stands at a distance x from the vertical line from point of suspension, then the magnitude of the electric field is

1.  $\frac{mg}{q}$

2.  $\frac{mg}{q}<mspace\; width="1em"></mspace>\frac{x}{l}$

3.  $\frac{mgx}{q\sqrt{l^2-x^2}}$

4.  $\frac{mgl}{q\sqrt{x^2<mspace\; width="1em"></mspace>-<mspace\; width="1em"></mspace>l^2}}$

Two identical small metal spheres having charges \(q\) and \(-3q\) exert force \(F\) on each other. The spheres are touched with each other and then kept at the same separation. The magnitude of the new force between the spheres will be:
1. \(\frac{4}{3}F\)
2. \(4F\)
3. \(2F\)
4. \(\frac{F}{3}\)

At what distance from the larger point charge the electric field is zero?

1.  4 cm

2.  11 cm

3.  22 cm

4.  40 cm

A point charge q is kept at the center of the circle formed by cutting a spherical shell by a plane as shown. The electric flux linked with the remaining surface of the shell is 

1.  $\varphi <mspace\; width="1em"></mspace><<mspace\; width="1em"></mspace>\frac{q}{2{\epsilon }_0}$

2.  $\varphi <mspace\; width="1em"></mspace>=<mspace\; width="1em"></mspace>\frac{q}{2{\epsilon }_0}$

3.  $\varphi <mspace\; width="1em"></mspace>>\frac{q}{2{\epsilon }_0}$

4.  $\varphi <mspace\; width="1em"></mspace>=<mspace\; width="1em"></mspace>\frac{q}{{\epsilon }_0}$

In the diagram shown below the block has charge q and is attached at one end of the light spring. The surface is smooth and horizontal and the spring is in its natural length. If the electric field E is switched on, the maximum elongation in the spring will be

1.  $\frac{qE}{2k}$

2.  $\frac{qE}{k}$

3.  $\frac{2qE}{k}$

4.  $\frac{4qE}{k}$

A point charge \(+q\) is kept at the center of the curvature of thin semicircular wire of length \(l\) as shown. The wire has uniformly distributed charge \(-q\) on it. The dipole moment of the system is

                  
1. \(\dfrac{2ql}{\pi^2}\)
2. \(\dfrac{2ql}{\pi}\)
3. \(\dfrac{\pi ql}{2}\)
4. zero

A conducting body has a cavity in its as shown in the diagram below. A point charge q is held at the centre of the cavity. The electric flux linked with the closed surface S (shown dotted) is

1.  $\frac{q}{{\epsilon }_0}$

2.  $\frac{q}{2{\epsilon }_0}$

3.  $\frac{q}{6{\epsilon }_0}$

4.  Zero