The electric potential at a point (x, y, z) is given by V = -x²y - xz³ +4 
The electric field $\overrightarrow{E}$ at that point is

1. $\overrightarrow{E}$= (2xy + z³)$\hat{\mathrm{i}}$ + x²$\hat{\mathrm{j}}$ + 3xz²$\hat{\mathrm{k}}$
2. $\overrightarrow{E}$ = 2xy$\hat{\mathrm{i}}$ + (x² +y²)$\hat{\mathrm{j}}$ +(3xz-y²)$\hat{\mathrm{k}}$
3. $\overrightarrow{E}$ = z³$\hat{\mathrm{i}}$ + xyz$\hat{\mathrm{j}}$ + z²$\hat{\mathrm{k}}$
4. $\overrightarrow{E}$ = (2xy- z³)$\hat{\mathrm{i}}$ + xy²$\hat{\mathrm{j}}$ + 3z²x$\hat{\mathrm{k}}$

Four electric charges +q, +q, -q and –q are placed at the corners of a square of side 2L (see figure). The electric potential at point A, mid-way between the two charges +q and +q is 
          

1.  $\frac{1}{4{\mathrm{\pi \epsilon }}_0}\frac{2\mathrm{q}}{\mathrm{L}}\left(1+\frac{1}{\sqrt{5}}\right)$

2.  $\frac{1}{4{\mathrm{\pi \epsilon }}_0}\frac{2\mathrm{q}}{\mathrm{L}}\left(1-\frac{1}{\sqrt{5}}\right)$

3.  zero

4.  $\frac{1}{4{\mathrm{\pi \epsilon }}_0}\frac{2\mathrm{q}}{\mathrm{L}}\left(1+\sqrt{5}\right)$

Three concentric spherical shells have radii a, b and c (a<b<c) and have surface charge densities $\mathrm{\sigma }, -\mathrm{\sigma }$ and $\mathrm{\sigma }$ respectively. If ${\mathrm{V}}_{\mathrm{A}}, {\mathrm{V}}_{\mathrm{B}}$ and ${\mathrm{V}}_{\mathrm{C}}$ denote the potential of the three shells, if c=a+b, we have

(1) ${\mathrm{V}}_{\mathrm{C}}={\mathrm{V}}_{\mathrm{A}}\ne {\mathrm{V}}_{\mathrm{B}}$                                       

(2) ${\mathrm{V}}_{\mathrm{C}}={\mathrm{V}}_B\ne {\mathrm{V}}_{\mathrm{A}}$

(3) ${\mathrm{V}}_{\mathrm{C}}\ne {\mathrm{V}}_B\ne {\mathrm{V}}_A$                                       

(4) ${\mathrm{V}}_{\mathrm{C}}={\mathrm{V}}_B={\mathrm{V}}_A$

A parallel plate air capacitor has a capacity of \(C\), the distance of separation between plates is \(d\) and potential difference \(V\) is applied between the plates. The force of attraction between the plates of the parallel plate air capacitor is:

The electrostatic force between the metal plates of an isolated parallel plate capacitor C having a charge Q and area A, is

1. Independent of the distance between the plates

2. linearly proportional to the distance between the plates

3. proportional to the sqaure root of the distance between the plates

4. inversely proportional to the distance between the plates

Charges +q and –q are placed at points A and B, respectively; which are at a distance 2L apart, C is the midpoint between A and B. The work done in moving a charge +Q along the semicircle CRD is : 
`

1. $\frac{qQ}{4{\mathrm{\pi \epsilon }}_0\mathrm{L}}$

2. $\frac{qQ}{2{\mathrm{\pi \epsilon }}_0\mathrm{L}}$

3. $\frac{qQ}{6{\mathrm{\pi \epsilon }}_0\mathrm{L}}$

4. $-\frac{qQ}{6{\mathrm{\pi \epsilon }}_0\mathrm{L}}$