An isolated solid metal sphere of radius R is given an electric charge. Which of the graphs below best shows the way in which the electric field E varies with distance x from the centre of the sphere?

1. 

2. 

3. 

4. 

The electric field intensity at P and Q in the shown arrangement are in the ratio of:

1. 1: 2

2. 2: 1

3. 1: 1

4. 4: 3

Consider an atom with atomic number Z as consisting of a positive point charge at the centre and surrounded by a distribution of negative charges uniformly distributed within a sphere of radius R. The electric field at a point inside the atom at a distance r from the centre is:

1. $\frac{\mathrm{Ze}}{4{\mathrm{\pi \epsilon }}_{0}0}\left[\frac{1}{{\mathrm{r}}^2}-\frac{\mathrm{r}}{{\mathrm{R}}^3}\right]$

2. $\frac{\mathrm{Ze}}{4{\mathrm{\pi \epsilon }}_0}\left[\frac{1}{{\mathrm{r}}^2}+\frac{1}{{\mathrm{R}}^3}\right]$

3. $\frac{2\mathrm{Ze}}{4{\mathrm{\pi \epsilon }}_0{\mathrm{r}}^2}$

4. Zero

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. $\frac{\mathrm{Force} \mathrm{between} \mathrm{them}}{2\mathrm{\pi r}}$

3. Force between them $\times 2\mathrm{\pi r}$

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