If ${\mathrm{q}}_{\mathrm{f}}$ is the free charge on the capacitor plates and ${\mathrm{q}}_{\mathrm{b}}$ is the bound charge on the dielectric slab of dielectric constant $\mathrm{k}$ placed between the capacitor plates, then bound charge ${\mathrm{q}}_{\mathrm{b}}$ can be expressed as :

Two ideal electric dipoles $A$ and $B$, having their dipole moment $p_1$ and $p_2$ respectively are placed on a plane with their centres at $O$ as shown in the figure. At point $C$ on the axis of dipole $A$, the resultant electric field is making an angle of $37°$ with the axis. The ratio of the dipole moment of $A$ and $B,\frac{p_1}{p_2}$ is$:($ take $\left.\sin 37°=\frac{3}{5}\right)$

In the given figure, a battery of emf $E$ is connected across a conductor $PQ$ of length $l$ and different area of cross-sections having radii $r_1$ and $r_2\left(r_2<r_1\right).$

Choose the correct option as one moves from $P$ to $Q$.

A capacitor of capacitance $C=1 \mu \mathrm{F}$ is suddenly connected to a battery of $100 \mathrm{V}$ through a resistance $R=100 \mathrm{\Omega }.$ The time taken for the capacitor to be charged to get $50 \mathrm{V}$ is:

(Take $\ln 2=0.69$)

In the reported figure, a capacitor is formed by placing a compound dielectric between the plates of parallel plate capacitor. The expression for the capacity of the said capacitor will be: (Given the area of the plate $=A$ )

A simple pendulum of mass ' $m$ ', length ' $l$ ' and charge $\text{'}+q^{\text{'}}$ suspended in the electric field produced by two conducting parallel plates as shown. The value of deflection of pendulum in equilibrium position will be

What will be the magnitude of the electric field at point $O$ as shown in the figure? Each side of the figure is $l$ and perpendicular to the other?