The potential at a certain point in an electric field is 200 V. The work done in carrying an electron upto that point will be.

1.  $3.2\times {10}^{-17}<mspace\; width="1em"></mspace>\mathrm{J}$                      

2.  $-3.2\times {10}^{-17}<mspace\; width="1em"></mspace>\mathrm{J}$

3.  $200<mspace\; width="1em"></mspace>\mathrm{J}$                                     

4.  $-200<mspace\; width="1em"></mspace>\mathrm{J}$

Two charged conducting spheres of radii ${\mathrm{r}}_1$ and ${\mathrm{r}}_2$ are at the same potential. The ratio of their surface charge densities will be -

1.  ${\mathrm{r}}_1/{\mathrm{r}}_2$                               

2.  ${\mathrm{r}}_2/{\mathrm{r}}_1$

3.  ${{\mathrm{r}}_1}^2/{{\mathrm{r}}_2}^2$                           

4.  ${{\mathrm{r}}_2}^2/{{\mathrm{r}}_1}^2$

At the mid point of a line joining an electron and a proton, the values of E and V will be.

1. $\mathrm{E}=0,<mspace\; width="1em"></mspace>\mathrm{V}\ne 0$                   

2. $\mathrm{E}\ne 0,<mspace\; width="1em"></mspace>\mathrm{V}=0$

3. $\mathrm{E}\ne 0,<mspace\; width="1em"></mspace>\mathrm{V}\ne 0$                   

4. $\mathrm{E}=0,<mspace\; width="1em"></mspace>\mathrm{V}=0$

A charge of $10\mu \mathrm{C}$ is kept at the origin of $\mathrm{X}–\mathrm{Y}$ coordinate system. The potential difference in volts between two points (a, 0) and $\left(\mathrm{a}/\sqrt{2}<mspace\; width="1em"></mspace>,<mspace\; width="1em"></mspace>\mathrm{a}/\sqrt{2}\right)$ will be.

1.  Zero                             

2.  $9\times {10}^4$

3.  $\frac{9\times {10}^4}{\mathrm{a}}$                           

4.  $\frac{9\times {10}^4}{\sqrt{2}}$

Find equivalent capacitance between $\mathrm{X}$ and $\mathrm{Y}$ if each capacitor is $4<mspace\; width="1em"></mspace>\mathrm{\mu F}$.

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

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

3.  $12<mspace\; width="1em"></mspace>\mathrm{\mu F}$                                   

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

Two point charge of $8<mspace\; width="1em"></mspace>\mathrm{\mu C}$ and $12<mspace\; width="1em"></mspace>\mathrm{\mu C}$ are kept in air at a distance of 10 cm from each other. The work required to change the distance between them to 6 cm will be.

1.  $5.8<mspace\; width="1em"></mspace>\mathrm{J}$                       

2.  $4.8<mspace\; width="1em"></mspace>\mathrm{J}$

3.  $3.8<mspace\; width="1em"></mspace>\mathrm{J}$                       

4.  $2.8<mspace\; width="1em"></mspace>\mathrm{J}$

Two parallel plate capacitors of capacitances C and 2C are connected in parallel and charged to a potential difference V. The battery is then disconnected and the region between the plates of the capacitor C is completely filled with a material of dielectric constant K. The potential difference across the capacitors now becomes –

1.  $\frac{3\mathrm{V}}{\mathrm{K}+2}$                             

2.  $\mathrm{KV}$

3.  $\frac{\mathrm{V}}{\mathrm{K}}$                                 

4.  $\frac{3}{\mathrm{KV}}$

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