(a) Two charged conducting spheres of radii $$a$$ and $$b$$ are connected to each other by a wire. Find the ratio of the electric fields at their surfaces.

OR

(b) A parallel plate capacitor (A) of capacitance C is charged by a battery to voltage $$V$$. The battery is disconnected and an uncharged capacitor (B) of capacitance $$2 \mathrm{C}$$ is connected across $$\mathrm{A}$$. Find the ratio of

(i) final charges on A and B.

(ii) total electrostatic energy stored in A and B finally and that stored in A initially.

Define current density and relaxation time. Derive an expression for resistivity of a conductor in terms of number density of charge carriers in the conductor and relaxation time.

A series CR circuit with $$R=200 \Omega$$ and $$C=(50 / \pi)$$ $$\mu \mathrm{F}$$ is connected across an ac source of peak voltage $$\varepsilon_0=100 \mathrm{~V}$$ and frequency $$v=50 \mathrm{~Hz}$$. Calculate (a) impedance of the circuit $$(\mathrm{Z})$$, (b) phase angle $$(\phi)$$, and (c) voltage across the resistor.

Define critical angle for a given pair of media and total internal reflection. Obtain the relation between the critical angle and refractive index of the medium.