1.
(a) What is meant by “Point Charge”? Can earth, being a charged sphere, be considered a point charge? (05)
(b) Define the term “flux” technically and scientifically. (08)
(c) A uniformly charged conducting sphere of 1.22m radius has surface charge density of \(8.13 \times 10^{-6} \text{ C/m}^2\). What is the total electric flux leaving the surface of the sphere? (07)

2.
(a) Give physical interpretation of Maxwell’s equations. (07)
(b) Briefly describe the applications of Maxwell’s equations. (07)
(c) Derive integral form of Maxwell’s equations:
            \(\nabla \cdot \vec{D} = \rho\) and \(\nabla \cdot \vec{B} = 0\)
(06)

3.
(a) Describe limitations of Coulomb’s law. (05)
(b) Consider the radioactive decay process: \(U_{92}^{238} \rightarrow He_2^4 + Th_{90}^{234}\). Calculate the force on \(\alpha\)-particle if its distance from the center of \(Th_{90}^{234}\) nucleus is \(1.2 \times 10^{-15}\text{m}\). (08)
(c) A proton is revolving around a negatively charged sphere with a speed \(v = 294\text{ km/s}\). If the radius of the sphere is \(1.13\text{cm}\), calculate the magnitude of charge on the sphere. (07)

4.
(a) What physical quantity oscillates in de Broglie wave? Discuss the importance of this periodic quantity. (06)
(b) Without mentioning the terms “electrons” and “atom”, give a general statement of Pauli’s Exclusion Principle. Elaborate its importance. (08)
(c) The location of an electron is approximated to an accuracy of \(0.0100\text{nm}\). Figure out: (i) the uncertainty in velocity? (ii) the corresponding kinetic energy in eV? (06)

5.
(a) Describe the process of formation of depletion region in a pn-junction. (06)
(b) Discuss the position and role of Fermi energy level in intrinsic, n-type and p-type semiconductor. (07)
(c) A \(5\Omega\) resistor and a diode are connected in series with a \(15\text{V}\) power supply as shown in Fig. 1 below. If the diode is ideal, determine the current that flows through it. (07)

6.
(a) Define thermionic emission. Also discuss its importance in science. (05)
(b) Discuss the functioning of two basic rectifier circuits. (07)
(c) Calculate the corresponding peak voltage \(V_{\text{peak}}\) of a domestic AC voltage. (07)

7.
(a) What are limitations of Bohr’s atomic model? (07)
(b) Give physical interpretation of the four quantum numbers, \(n, l, m_l\) and \(m_s\). (08)
(c) The general expression of the radiation of wavelength \(\lambda\) in the Bohr’s model is:

\(\lambda = \frac{n_1^2 n_2^2}{(n_2^2 – n_1^2) R}\)

Calculate the expression for the \(\lambda_{\text{min}}\) by taking \(n_1 = 1\) and \(n_2 = \infty\). (05)

8.
(a) What is a mass spectrometer? How can it be exploited in Nuclear Physics. (06)
(b) Give a brief account of Nuclear Shell Model. (07)
(c) Consider two nuclei, \(\text{(Nucleus)}_A\) and \(\text{(Nucleus)}_B\), with similar charge number and mass number but different binding energies. If \(\text{(BE)}_A > \text{(BE)}_B\), which nucleus will have more mass and why? (07)