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. \( 900~\mu\text{C}\)

Three charges \(-Q\), \(q\), and \(-2Q\) are placed along a line as shown in the figure. The system of charges will have a positive potential energy configuration when q is placed at midpoint of line joining \(-Q\) and \(-2Q\), if:
      

The electric field intensity and the electric potential at a point are E and V respectively. Which of the following is correct?

Work done to carry a negatively charged body in direction of the electric field:
(assuming no other force is acting on the body)

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. \( \frac{5}{3}C\)

Surface charge density on the positive plate of a charged parallel plate capacitor is $\sigma$. Energy density in the electric field of the capacitor is:

1. $\frac{{\sigma }^2}{{\epsilon }_0}$

2. $\frac{{\sigma }^2}{2{\epsilon }_0}$

3. $\frac{\sigma }{{\epsilon }_0}$

4. $2{\sigma }^2{\epsilon }_0$

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:

How many capacitors each of $8$ $\mu F$ and 250 V are required to form a composite capacitor of $16$ $\mu F$ and 1 kV?

A positive charge q and a negative charge -q are placed at x= -a and x= +a respectively. The variation of V along x-axis is represented by the graph:

1.		2.
3.		4.