An electron is rotating around an infinite positive linear charge in a circle of radius 0.1 m. If the linear charge density is 1 $\mathrm{\mu C}/\mathrm{m}$, then the velocity of the electron in m/s will be:

1. $0.582\times {10}^7$

2. $5.62\times {10}^7$

3. $562\times {10}^7$

4. $0.0562\times {10}^7$

For two infinitely long charged parallel sheets, the electric field at P will be:

1. $\frac{\mathrm{\sigma }}{2\mathrm{x}}-\frac{\mathrm{\sigma }}{2(\mathrm{r}-\mathrm{x})}$

2. $\frac{\mathrm{\sigma }}{2{\mathrm{\epsilon }}_0\mathrm{x}}+\frac{\mathrm{\sigma }}{2\mathrm{\pi }(\mathrm{r}-\mathrm{x}){\mathrm{\epsilon }}_0}$

3. $\frac{\mathrm{\sigma }}{{\mathrm{\epsilon }}_0}$

4. Zero

When a test charge is brought in from infinity along the perpendicular bisector of an electric dipole, the work done is:

1. Positive

2. Zero

3. Negative

4. None of these

Two small spheres each carrying a charge q are placed at distance r apart. If one of the spheres is taken around the other in a circular path, the work done will be equal to:

1. Force between them $\times$ r

2. $\frac{\mathrm{Force}<mspace\; width="1em"></mspace>\mathrm{between}<mspace\; width="1em"></mspace>\mathrm{them}}{2\mathrm{\pi r}}$

3. Force between them $\times <mspace\; width="1em"></mspace>2\mathrm{\pi r}$

4. Zero

Work done in moving a charge q coulomb on the surface of a given charged conductor of potential V is:

1. $\frac{\mathrm{V}}{\mathrm{q}}$ joule

2. $\mathrm{Vq}$ joule

3. $\frac{\mathrm{q}}{\mathrm{V}}$ joule

4. Zero

The variation of electric field between the two charges q₁ and q₂ along the line joining the charges is plotted against distance from q₁ (taking rightwards direction of field as positive) as shown, then the correct statement is:

1. q₁ and q₂ are positive and q₁ < q₂

2. q₁ and q₂ are positive and q₁ > q₂ 

3. q₁ is positive and q₂ is negative 

4. q₁ is positive and q₂ is negative  and  q₁ < |q₂|

Two identical infinite positive line charges are placed along the lines $x=\pm a$, in the x-y plane. A positive point charge placed at origin is restricted to move along y-axis. Its equilibrium is:

1. Stable

2. Neutral

3. Unstable

4. None of these

In the figure below, a point charge +Q₁ is at the centre of an imaginary spherical Gaussian surface and another point charge +Q₂ is outside of the Gaussian surface. Point P is on the surface of the sphere. Which one of the following statements is true ?

1. Both charges +Q₁ and +Q₂ contribute to the net electric flux through the sphere but only charge +Q₁ contributes to the electric field at point P on the sphere.

2. Both charges +Q₁ and +Q₂ contribute to the net electric flux through the sphere but +Q₂ contributes to the electric field at point P on the sphere.

3. Only the charge +Q₁ contributes to the net electric flux through the sphere but both charges +Q₁ and +Q₂ contribute to the electric field at point P.

4. Only the charge +Q₂ contributes to the net electric flux through the sphere but both charges +Q₁ and +Q₂ contribute to the electric field at point P.

In a Millikan-type experiment, there are two oil droplets P and Q between the charged horizontal plates, as shown in the diagram. Droplet P is in rest while droplet Q is moving upwards. The polarity of the charges on P and Q is

                     P                Q

1.                  +                +

2.             Neutral              -

3.                  -                  - 

4.                  +                 -

In the electric field of a point charge q, a certain charge is carried from point A to B, C, D, and E, the work done:

1. is least along the path AB

2. is least along the path AD

3. is zero along any one of the paths AB, AC and AE

4. is least along AE.