A capacitor of \(2~\mu\text{F}\) is charged as shown in the figure. When the switch \(S\) is turned to position \(2\), the percentage of its stored energy dissipated is:
         

1.	\(20\%\)	2.	\(75\%\)
3.	\(80\%\)	4.	\(0\%\)

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$\hat{j}$+$\hat{\mathrm{k}}$) 

A parallel plate air capacitor has capacity C, distance of separation between plates is d and potential difference V is applied between the plates. Force of attraction between the plates of the parallel plate air capacitor is

(1)C²V²/2d

(2)CV²/2d

(3)CV²/d

(4)C²V²/2d²

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

(a) zero and Q/4π$\epsilon$_oR² 

(b)Q/4π$\epsilon$_oR and zero

(c)Q/4π$\epsilon$_oR and Q/4π$\epsilon$_oR²

(d)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 $-Q,-q,2q and 2Q$ 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. \(1\times 10^{-2}~\text{C}\)