The diagrams below show regions of equipotentials.

  

A positive charge is moved from \(\mathrm A\) to \(\mathrm B\) in each diagram. Then:

1.	the maximum work is required to move \(q\) in figure(iii).
2.	in all four cases, the work done is the same.
3.	the minimum work is required to move \(q\) in the figure(i).
4.	the maximum work is required to move \(q\) in figure(ii).

An electric dipole is place at an angle of \(30^{\circ}\) with an electric field intensity \(2\times10^{5}~\text{N/C}\). It experiences a torque equal to \(4~\text{Nm}\). The charge on the dipole, if the dipole length is \(2~\text{cm}\), is: 

A parallel-plate capacitor of area A, plate separation d, and capacitance C is filled with four dielectric materials having dielectric constants $k_1,k_2,k_3$ $$and $k_4$ as shown in the figure below. If a single dielectric material is to be used to have the same capacitance C in this capacitor, then its dielectric constant k is given by

(a) $\mathrm{k}={\mathrm{k}}_1+{\mathrm{k}}_2+{\mathrm{k}}_3+3{\mathrm{k}}_4$

(b) $k=\frac{2}{3}\left(k_1+k_2+k_3\right)+2k_4$

(c) $\frac{1}{k}=\frac{3}{2\left(k_1+k_2+k_3\right)}+\frac{1}{2k_4}$

(d) $\frac{1}{\mathrm{k}}=\frac{1}{{\mathrm{k}}_1}+\frac{1}{{\mathrm{k}}_2}+\frac{1}{{\mathrm{k}}_3}+\frac{3}{2{\mathrm{k}}_4}$

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:
         

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