BE Computer Engineering (Pokhara University) Applied Physics (PU, PHY 110) Question Paper 2079

(a) Set up the differential equation of a damped harmonic oscillator and obtain its solution for the under-damped (weakly damped) case. Hence explain the terms under-damping, critical damping and over-damping with appropriate displacement–time sketches. (9)

(b) A body of mass 0.2 kg executes damped oscillations with a force constant of 80 N/m and a damping constant of 0.16 kg/s. Calculate the angular frequency of the damped oscillation and the time in which the amplitude falls to half of its initial value. (5)

(a) State Maxwell's equations of electromagnetism in differential form and explain the physical significance of each. Show how Maxwell modified Ampere's law by introducing the concept of displacement current. (8)

(b) Starting from Maxwell's equations in free space, derive the wave equation for the electric field and hence obtain an expression for the speed of electromagnetic waves in vacuum. (6)

(a) Derive the time-independent Schrödinger wave equation for a particle of mass m moving in a region of potential energy V. (6)

(b) Apply the Schrödinger equation to a particle confined in a one-dimensional infinite potential well (rigid box) of width L. Obtain the normalized wave functions and show that the energy of the particle is quantized. Sketch the first three energy eigenstates. (6)

(a) Explain the principle of light propagation through an optical fibre based on total internal reflection. Define acceptance angle and numerical aperture, and derive an expression for the numerical aperture in terms of the refractive indices of the core and cladding. (8)

(b) An optical fibre has a core refractive index of 1.50 and a cladding refractive index of 1.46. Calculate its numerical aperture and the acceptance angle when the fibre is placed in air. (4)

Explain the formation of Newton's rings in reflected light. Derive an expression for the diameter of the n-th dark ring and show how the wavelength of monochromatic light can be determined using this arrangement.

What is a plane diffraction grating? Obtain the grating equation for the position of principal maxima. A grating having 5000 lines per cm is illuminated normally by light of wavelength 589 nm; find the angle of diffraction for the second-order maximum.

(a) State and explain Brewster's law and use it to define the polarizing angle. (4)

(b) Distinguish between a quarter-wave plate and a half-wave plate, stating one practical use of each. (3)

Explain the terms spontaneous emission, stimulated emission and population inversion. Why is population inversion essential for laser action, and how is it achieved in a three-level laser system?

Describe the formation of a depletion region in an unbiased p–n junction diode. Explain qualitatively, with the help of energy-band diagrams, how the junction behaves under forward bias and reverse bias.

State the Hall effect and derive an expression for the Hall coefficient. Mention two important applications of the Hall effect in characterizing semiconductor materials.

Explain the different types of polarization mechanisms in a dielectric material. Derive the Clausius–Mossotti relation connecting the dielectric constant of a material to its atomic polarizability.

Distinguish between diamagnetic, paramagnetic and ferromagnetic materials on the basis of their magnetic susceptibility and behaviour in an external magnetic field, giving one example of each.

State Heisenberg's uncertainty principle. Using it, estimate the minimum energy (zero-point energy) of an electron confined within a nucleus of dimension 10⁻¹⁴ m and comment on whether electrons can exist inside the nucleus.