Maximum charge stored on a metal sphere of radius $15$ cm may be $7.5<mspace\; width="1em"></mspace>\mu \mathrm{C}$. The potential energy of the sphere in this case is :

1.  $9.67<mspace\; width="1em"></mspace>\mathrm{J}$                   

2.  $0.25<mspace\; width="1em"></mspace>\mathrm{J}$ 

3.  $3.25<mspace\; width="1em"></mspace>\mathrm{J}$                    

4.  $1.69<mspace\; width="1em"></mspace>\mathrm{J}$

Four identical particles each of mass m and charge q are kept at the four corners of a square of length L. The final velocity of these particles after setting them free will be.

1. ${\left[\frac{{\mathrm{Kq}}^2}{\mathrm{mL}}\left(5.4\right)\right]}^{1/2}$                           

2. ${\left[\frac{{\mathrm{Kq}}^2}{\mathrm{mL}}\left(1.35\right)\right]}^{1/2}$

3. ${\left[\frac{{\mathrm{Kq}}^2}{\mathrm{mL}}\left(2.7\right)\right]}^{1/2}$                           

4. Zero

A parallel plate capacitor is charged to a certain potential difference. A slab of thickness 3 mm is inserted between the plates and it becomes necessary to increase the distance between the plates by 2.4 mm to maintain the same potential difference. The dielectric constant of the slab is– 

1.  3                   

2.  5 

3.  2.5               

4.  2

A charge $\mathrm{Q}$ is distributed over two concentric hollow spheres of radii r and $\mathrm{R}<mspace\; width="1em"></mspace>\left(\mathrm{R}<mspace\; width="1em"></mspace>><mspace\; width="1em"></mspace>\mathrm{r}\right)$ such that the surface densities are equal. The potential at the common centre is $\frac{1}{4{\mathrm{\pi \epsilon }}_0}$ times –

1.  $\mathrm{Q}<mspace\; width="1em"></mspace>\left(\frac{\mathrm{r}+\mathrm{R}}{{\mathrm{r}}^2+{\mathrm{R}}^2}\right)$                       

2.  $\frac{\mathrm{Q}}{2}<mspace\; width="1em"></mspace>\left(\frac{\mathrm{r}+\mathrm{R}}{{\mathrm{r}}^2+{\mathrm{R}}^2}\right)$

3.  $2\mathrm{Q}<mspace\; width="1em"></mspace>\left(\frac{\mathrm{r}+\mathrm{R}}{{\mathrm{r}}^2+{\mathrm{R}}^2}\right)$                     

4.  Zero

A charge $+\mathrm{Q}$ is uniformly distributed over a thin ring of radius $\mathrm{R}$, velocity of an electron at the moment it passes through the centre $\mathrm{O}$ of the ring, if the electron was initially at rest at a point $\mathrm{A}$ which is very far away from the centre and on the axis of the ring is

1. $\sqrt{\frac{2\mathrm{kQe}}{\mathrm{mR}}}$                     

2. $\sqrt{\frac{\mathrm{kQe}}{\mathrm{m}}}$

3. $\sqrt{\frac{\mathrm{kme}}{\mathrm{QR}}}$                       

4. $\sqrt{\frac{\mathrm{kQe}}{\mathrm{mR}}}$

The electric potential V as a function of distance x (in metre) is given by: $\mathrm{V}=\left(5{\mathrm{x}}^2+10\mathrm{x}-9\right)<mspace\; width="1em"></mspace>\mathrm{V}.$ The value of the electric field of x = 1m would be -

1.  $20<mspace\; width="1em"></mspace>\mathrm{V}/\mathrm{m}$                 

2.  $6<mspace\; width="1em"></mspace>\mathrm{V}/\mathrm{m}$

3.  $11<mspace\; width="1em"></mspace>\mathrm{V}/\mathrm{m}$                 

4.  $-23<mspace\; width="1em"></mspace>\mathrm{V}/\mathrm{m}$

An uncharged capacitor with a solid dielectric is connected to a similar air capacitor charged to a potential of ${\mathrm{V}}_0$. If the common potential after sharing of charges becomes $\mathrm{V}$, then the dielectric constant of the dielectric must be –

1. $\frac{{\mathrm{V}}_0}{\mathrm{V}}$                               

2. $\frac{\mathrm{V}}{{\mathrm{V}}_0}$

3. $\frac{{\mathrm{V}}_0-\mathrm{V}}{\mathrm{V}}$                         

4. $\frac{{\mathrm{V}}_0-\mathrm{V}}{{\mathrm{V}}_0}$

Two parallel conducting plates $5\mathrm{mm}$ apart are held horizontally one above the other. The upper plate is maintained at a positive potential of $15<mspace\; width="1em"></mspace>\mathrm{kV}$ while the lower plate is earthed. If a small oil drop of relative density $0.92$ and of radius $5<mspace\; width="1em"></mspace>\mu \mathrm{m}$ remains stationary between the plates, then the charge on the drop will be.

1.  $10\mathrm{e}$                     

2.  $8\mathrm{e}$ 

3.  $5\mathrm{e}$                       

4.  $3\mathrm{e}$

An infinite number of charges (each of magnitude $1<mspace\; width="1em"></mspace>\mu \mathrm{c}$) are placed along the $\mathrm{X}$-axis at x = 1, 2, 4, 8....metre. If the charges are alternately of opposite sign, then the potential at the point x = 0 due to these charges will be.

1.  $6\times {10}^3<mspace\; width="1em"></mspace>\mathrm{V}$                       

2.  $9\times {10}^3<mspace\; width="1em"></mspace>\mathrm{V}$

3.  $1.8\times {10}^4<mspace\; width="1em"></mspace>\mathrm{V}$                   

4.  $1.2\times {10}^4<mspace\; width="1em"></mspace>\mathrm{V}$