Five identical plates each of area A are joined as shown in the figure. The distance between the plates is d. The plates are connected to a potential difference of V volts. The charge on plates 1 and 4 will be:

1. $\frac{{\epsilon }_{0}AV}{d}, \frac{2{\epsilon }_{0}AV}{d}$

2. $\frac{{\epsilon }_{0}AV}{d}, \frac{2{\epsilon }_{0}AV}{d}$

3. $$ $\frac{{\epsilon }_{0}AV}{d}, \frac{-2{\epsilon }_{0}AV}{d}$

4. $\frac{-{\epsilon }_{0}AV}{d}, \frac{-2{\epsilon }_{0}AV}{d}$

A network of four capacitors of capacity equal to $C_1=C,$ $C_2=2C,$ $C_3=3C$ and C₄ = 4C are connected in a battery as shown in the figure. The ratio of the charges on C₂ and C₄ is:
       
1. $\frac{22}{3}$

2. $\frac{3}{22}$

3. $\frac{7}{4}$

4. $\frac{4}{7}$

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:

The equivalent capacitance between points a and b in the network shown below is:

1. 5C

2. 4C

3. 3C

4. 2C

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

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