A parallel plate air capacitor of capacitance \(C\) is connected to a cell of emf \(V\) and then disconnected from it. A dielectric slab of dielectric constant \(K\), which can just fill the air gap of the capacitor, is now inserted in it. Which of the following is incorrect?

1.	The potential difference between the plates decreases \(K\) times
2.	The energy stored in the capacitor decreases \(K\) times
3.	The change in energy stored is \({1 \over 2} CV^{2}(\frac{1}{K}-1)\)
4.	The charge on the capacitor is not conserved

If potential (in volts) in a region is expressed as V(x,y,z)=6xy-y+2yz, the electric field (in N/C) at point (1,1,0) is       

1. (3$\hat{i}$+5$\hat{j}$+3$\hat{\mathrm{k}}$)

2. (6$\hat{i}$+5$\hat{j}$+2$\hat{\mathrm{k}}$)

3. (2$\hat{i}$+3$\hat{j}$+$\hat{\mathrm{k}}$)

4. (6$\hat{i}$+9$\hat{j}$+$\hat{\mathrm{k}}$) 

Two thin dielectric slabs of dielectric constants K₁&K₂ ($K_1<K_2$) are inserted between plates of a parallel capacitor, as shown in the figure. The variation of electric field E between the plates with distance d as measured from plate P is correctly shown by  

1.

2. 

3.

4.

A conducting sphere of radius R is given a charge Q. The electric potential and field at the centre of the sphere respectively are

1. zero and Q/4π$\epsilon$_oR² 

2. Q/4π$\epsilon$_oR and zero

3. Q/4π$\epsilon$_oR and Q/4π$\epsilon$_oR²

4. Both are zero

In a region, the potential is represented by V(x,y,z)=6x-8xy-8y+6yz, where V is in volts and x,y,z are in meters. The electric force experienced by a charge of 2 coulomb situated at point (1,1,1) is

1. 6√5N
 

2. 30N
 

3. 24N
 

4. 4√35N

\(A,B\) and \(C\) are three points in a uniform electric field. The electric potential is:
               

Four point charges $-Q,-q,2q<mspace\; width="1em"></mspace>and<mspace\; width="1em"></mspace>2Q$ are placed, one at each corner of the square. The relation between Q and q for which the potential at the centre of the square is zero, is 

1. Q=-q                                       

2. Q=-$\frac{1}{q}$

3. Q=q                                         

4. Q=$\frac{1}{q}$

Two metallic spheres of radii \(1\) cm and \(3\) cm are given charges of \(-1\times 10^{-2}~\text{C}\) and \(5\times 10^{-2}~\text{C},\) respectively. If these are connected by a conducting wire, the final charge on the bigger sphere is:
1. \(2\times 10^{-2}~\text{C}\)
2. \(3\times 10^{-2}~\text{C}\)
3. \(4\times 10^{-2}~\text{C}\)
4. \(1\times 10^{-2}~\text{C}\)

A parallel plate condenser has a uniform electric field \(E\)(V/m) in the space between the plates. If the distance between the plates is \(d\)(m) and area of each plate is \(A(\text{m}^2)\), the energy (joule) stored in the condenser is:

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