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

   

1.		2.
3.		4.

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 a point \((1,1,1)\) is:
1. \(6\sqrt{5}~\text{N}\)
2. \(30~\text{N}\)
3. \(24~\text{N}\)
4. \(4\sqrt{35}~\text{N}\)

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

     

1.	maximum at \(B\)
2.	maximum at \(C\)
3.	same at all the three points \(A, B\) and \(C\)
4.	maximum at \(A\)

An electric dipole of moment \(p\) is placed in an electric field of intensity \(E.\) The dipole acquires a position such that the axis of the dipole makes an angle \(\theta\) with the direction of the field. Assuming that the potential energy of the dipole to be zero when \(\theta = 90^{\circ}\)$$, the torque and the potential energy of the dipole will respectively be:
1. \(pE\text{sin}\theta, ~-pE\text{cos}\theta\)
2. \(pE\text{sin}\theta, ~-2pE\text{cos}\theta\)
3. \(pE\text{sin}\theta, ~2pE\text{cos}\theta\)
4. \(pE\text{cos}\theta, ~-pE\text{sin}\theta\)

Three capacitors each of capacitance \(C\) and of breakdown voltage \(V\) are joined in series. The capacitance and breakdown voltage of the combination will be:
1. $\frac{C}{3},$ $\frac{V}{3}$

2. $3C,$ $\frac{V}{3}$

3. $\frac{C}{3},$ $3V$

4. \(3C,~3V\)

The electric potential at a point in free space due to a charge \(Q\) coulomb is \(Q\times10^{11}~\text{V}\). The electric field at that point is:
1. \(4\pi \varepsilon_0 Q\times 10^{22}~\text{V/m}\)
2. \(12\pi \varepsilon_0 Q\times 10^{20}~\text{V/m}\)
3. \(4\pi \varepsilon_0 Q\times 10^{20}~\text{V/m}\)
4. \(12\pi \varepsilon_0 Q\times 10^{22}~\text{V/m}\)

Two condensers, one of capacity \(C\) and the other of capacity \(\frac{C}2\) are connected to a \(V\) volt battery, as shown in the figure. 
           
The energy stored in the capacitors when both condensers are fully charged will be:
1. \(2CV^2\)
2. \({1 \over4}CV^2\)
3. \({3 \over4}CV^2\)
4. \({1 \over2}CV^2\)

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

An electric dipole of moment \(\vec {p} \) is lying along a uniform electric field \(\vec{E}.\) The work done in rotating the dipole by \(90^{\circ}\) is:
1. \(\sqrt{2}pE\)
2. \(\dfrac{pE}{2}\)
3. \(2pE\)
4. \(pE\)