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.
(a) (i) Distinguish between nuclear fission and fusion giving an example of each.
(ii) Explain the release of energy in nuclear fission and fusion on the basis of binding energy per nucleon curve.
OR
(b) (i) How is the size of a nucleus found experimentally? Write the relation between the radius and mass number of a nucleus.
(ii) Prove that the density of a nucleus is independent of its mass number.
(a) (i) Use Gauss' law to obtain an expression for the electric field due to an infinitely long thin straight wire with uniform linear charge density $$\lambda$$.
(ii) An infinitely long positively charged straight wire has a linear charge density $$\lambda$$. An electron is revolving in a circle with a constant speed $$v$$ such that the wire passes through the centre, and is perpendicular to the plane, of the circle. Find the kinetic energy of the electron in terms of magnitudes of its charge and linear charge density $$\lambda$$ on the wire.
(iii) Draw a graph of kinetic energy as a function of linear charge density $$\lambda$$.
OR
(b) (i) Consider two identical point charges located at points $$(0,0)$$ and $$(a, 0)$$.
(1) Is there a point on the line joining them at which the electric field is zero?
(2) Is there a point on the line joining them at which the electric potential is zero?
Justify your answers for each case.
(ii) State the significance of negative value of electrostatic potential energy of a system of charges.
Three charges are placed at the corners of an equilateral triangle $$A B C$$ of side $$2.0 \mathrm{~m}$$ as shown in figure. Calculate the electric potential energy of the system of three charges.
