Two capacitors of capacitance \(6~\mu\text{F}\) and \(3~\mu\text{F}\) are connected in series with battery of \(30~\text{V}\). The charge on \(3~\mu\text{F}\) capacitor at a steady state is:
        
1. \( 3 ~\mu\text{C}\)
2. \( 1.5 ~\mu\text{C}\)
3. \( 60~\mu\text{C}\)
4. \( 900~\mu\text{C}\)

Two concentric metallic spherical shells A and B of radii a and b respectively (b>a) are arranged such that outer shell is earthed and inner shell is charged to Q. Charge on the outer surface of outer shell will be:

1. $-\frac{Qa}{b}$

2. $Q\left(1-\begin{array}{c}\frac{a}{b}\end{array}\right)$

3. -Q

4. zero

The equivalent capacitance across \(A\) and \(B\) in the given figure is:

  
1. \( \frac{3}{2}C\)
2. \(C\)
3. \( \frac{2}{3}C\)
4. \( \frac{5}{3}C\)

Two capacitors of capacity $2$ $\mu F$ and $3$ $\mu F$ are charged to the same potential difference of 6 V. Now they are connected with opposite polarity as shown. After closing switches $S_1$ $and$ $S_2$, their final potential difference becomes:

Which of the following statements is correct regarding electrostatics of conductors?

The equivalent capacitance of the following arrangement is:
               
1. $18$ $\mu F$
2. $9$ $\mu F$
3. $6$ $\mu F$
4. $12$ $\mu F$

Some equipotential surfaces are shown in figure. The electric field at points A, B and C are respectively:

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:

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

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.