The figure shows some of the equipotential surfaces. Magnitude and direction of the electric field is given by

                                  

1. 200 V/m, making an angle ${120}^{\circ }$with the x-axis

2. 100 V/m, pointing towards negative x-axis

3. 200 V/m, making an angle $-{60}^{\circ }$with the x-axis

4. 100 V/m, making an angle ${30}^{\circ }$ with the x-axis

 

Electric field in a region is increasing in magnitude along x-direction. The equipotential surfaces associated are :

1. Planes parallel to xy-plane

2. Planes parallel to yz-plane 

3. Co-axial cylinders around the x-axis

4. All of these

If a unit positive charge is taken from one point to another on an equipotential surface, then

1. Work is done on the charge

2. Work is done by the charge

3. Potential energy of the charged is changed

4. No work is done on the charge

Four charges of \(+1~\mu\text{C}\), \(+1~\mu\text{C}\), \(-1~\mu\text{C}\) and \(+1~\mu\text{C}\) are placed at the vertices of a square of side \(\sqrt{2}~\text{cm}\), in sequence. The net force experienced by \(0.1~\mu\text{C}\) charge at the centre of square:
1. \(9~\text{N}\)
2. \(18~\text{N}\)
3. \(36~\text{N}\)
4.  Zero

Two short dipoles are placed at a certain distance exert a force 'F' on each other. If the distance between them is doubled then the force will become

1.  F

2.  $\frac{F}{4}$

3.  4F

4.  $\frac{F}{16}$

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

1. \(q\times 2a\)

2. \(2q \times 2a\)

3. \(q\times a\)

4. \(2\times (2q\times 2a)\)

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. \(\frac{F}{3}\)