The true statement is, on increasing the distance between the plates of a parallel plate condenser -

(1) The electric intensity between the plates will decrease

(2) The electric intensity between the plates will increase

(3) The electric intensity between the plates will remain unchanged

(4) The P.D. between the plates will decrease

In a certain charge distribution, all points having zero potential can be joined by a circle S. Points inside S have positive potential, and points outside S have a negative potential. A positive charge, which is free to move, is placed inside S .

(1) It will remain in equilibrium

(2) It can move inside S, but it cannot cross S

(3) It must cross S at some time

(4) It may move, but will ultimately return to its starting point

Two concentric, thin metallic spheres of radii ${\mathrm{R}}_1$ and ${\mathrm{R}}_2$ $\left({\mathrm{R}}_1 > {\mathrm{R}}_2\right)$ bear changes ${\mathrm{Q}}_1$ and ${\mathrm{Q}}_2$ respectively. Then the potential at distance r between ${\mathrm{R}}_1$ and ${\mathrm{R}}_2$ will be $\left(\mathrm{k}=\frac{1}{4{\mathrm{\pi \epsilon }}_0}\right)$

1.  $\mathrm{k} \left(\frac{{\mathrm{Q}}_1+{\mathrm{Q}}_2}{\mathrm{r}}\right)$                       

2.  $\mathrm{k} \left(\frac{{\mathrm{Q}}_1}{\mathrm{r}}+\frac{{\mathrm{Q}}_2}{{\mathrm{R}}_2}\right)$

3.  $\mathrm{k} \left(\frac{{\mathrm{Q}}_2}{\mathrm{r}}+\frac{{\mathrm{Q}}_1}{{\mathrm{R}}_1}\right)$                     

4.  $\mathrm{k} \left(\frac{{\mathrm{Q}}_1}{{\mathrm{R}}_1}+\frac{{\mathrm{Q}}_1}{{\mathrm{R}}_2}\right)$

A parallel plate capacitor is connected to a battery. The plates are pulled apart with a uniform speed. If x is the separation between the plates, the time rate of change of electrostatic energy of the capacitor is proportional to:

(1) x^–2

(2) x

(3) x^–1

(4) x²

n identical condensers are joined in parallel and are charged to potential V. Now they are separated and joined in series. Then the total energy and potential difference of the combination will be 

(1) Energy and potential difference remain the same

(2) Energy remains the same and the potential difference is nV

(3) Energy increases n times and potential difference is nV

(4) Energy increases n times and potential difference remains the same

Consider two points 1 and 2 in a region outside a charged sphere. Two points are not very far away from the sphere. If E and V represent the electric field vector and the electric potential, which of the following is not possible 

(1) $\left|{\overrightarrow{E}}_1\right|=\left|{\overrightarrow{E}}_2\right|,V_1=V_2$

(2) ${\overrightarrow{E}}_1\ne {\overrightarrow{E}}_2,V_1\ne V_2$

(3) ${\overrightarrow{E}}_1\ne {\overrightarrow{E}}_2,V_1=V_2$

(4) $\left|{\overrightarrow{E}}_1\right|=\left|{\overrightarrow{E}}_2\right|,V_1\ne V_2$

A capacitor of capacity C₁ is charged to the potential of V₀. On disconnecting with the battery, it is connected with a capacitor of capacity C₂ as shown in the adjoining figure. The ratio of energies before and after the connection of switch S will be

(1) (C₁ + C₂)/C₁

(2) C₁/(C₁ + C₂)

(3) C₁C₂

(4) C₁/C₂

Two identical thin rings each of radius R meters are coaxially placed at a distance R meters apart. If Q₁ coulomb and Q₂ coulomb are respectively the charges uniformly spread on the two rings, the work done in moving a charge q from the centre of one ring to that of other is 

(1) Zero

(2) $\frac{q(Q_2-Q_1)(\sqrt{2}-1)}{\sqrt{2}.4\pi {\epsilon }_{0}R}$

(3) $\frac{q\sqrt{2}(Q_1+Q_2)}{4\pi {\epsilon }_{0}R}$

(4) $\frac{q(Q_1+Q_2)(\sqrt{2}+1)}{\sqrt{2}.4\pi {\epsilon }_{0}R}$

A solid conducting sphere having a charge Q is surrounded by an uncharged concentric conducting hollow spherical shell. Let the potential difference between the surface of the solid sphere and that of the outer surface of the hollow shell be V. If the shell is now given a charge of –3Q, the new potential difference between the same two surfaces is 

(1) V

(2) 2V

(3) 4V

(4) –2V