BE Computer Engineering (IOE, TU) Engineering Physics (IOE, SH 452) Question Paper 2078

(a) Set up the differential equation of a damped harmonic oscillator and obtain its solution for the underdamped case. Explain the significance of the damping constant. [7]

(b) The quality factor of a tuning fork of frequency 256 Hz is 1000. Calculate the time after which its energy of vibration becomes 1/e of its initial value, and the energy lost in the first second of vibration. [5]

(a) Write down Maxwell's equations in differential form and state the physical law each one represents. Show how the concept of displacement current makes Ampere's law consistent with the equation of continuity. [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 velocity of an electromagnetic wave in vacuum. [4]

(a) Describe, with a neat ray diagram, the formation of Newton's rings by reflected light. Derive expressions for the radii of the dark and bright rings and explain why the centre of the ring system is dark. [8]

(b) In a Newton's rings experiment the diameter of the 10th dark ring is 0.50 cm and that of the 20th dark ring is 0.70 cm. If the radius of curvature of the lens is 100 cm, find the wavelength of the light used. [4]

(a) Derive the time-independent Schrodinger wave equation for a particle moving in one dimension. State the conditions a wave function must satisfy to be physically acceptable. [7]

(b) A particle is confined to a one-dimensional infinite potential well of width L. Solve the Schrodinger equation for this system to obtain the normalized wave functions and the allowed energy eigenvalues. [5]

Discuss the phenomenon of resonance in a forced mechanical oscillator. Derive the expression for the amplitude of forced vibration and show that the amplitude is maximum at the resonant frequency. Sketch the resonance curves for different values of damping.

(a) What is meant by plane, circularly and elliptically polarized light? [3]

(b) Explain the construction and working of a Nicol prism and state how it can be used as a polarizer and an analyzer. [5]

(a) What is a plane diffraction grating? Obtain the grating equation for the position of principal maxima. [5]

(b) A diffraction grating has 5000 lines per cm. Find the angle of diffraction for the second-order maximum of light of wavelength 5890 angstrom. [3]

(a) Explain the terms spontaneous emission, stimulated emission and population inversion. Why is population inversion essential for laser action? [5]

(b) With a neat energy-level diagram, explain the working of a He-Ne laser. [3]

(a) Define acceptance angle and numerical aperture of an optical fibre and derive the relation between them in terms of the refractive indices of the core and cladding. [5]

(b) An optical fibre has a core of refractive index 1.50 and a cladding of refractive index 1.47. Calculate its numerical aperture and acceptance angle. [3]

(a) Define electric polarization and electric displacement. Establish the relation D = ε₀E + P and hence relate the dielectric constant to the electric susceptibility. [5]

(b) A parallel-plate capacitor with plate area 100 cm² and separation 1 mm is filled with a dielectric of relative permittivity 5. Calculate its capacitance. [3]

(a) State and explain Heisenberg's uncertainty principle. Using it, show that an electron cannot exist inside an atomic nucleus. [5]

(b) Calculate the de Broglie wavelength of an electron accelerated through a potential difference of 100 V. [3]

(a) What is the Hall effect? Derive an expression for the Hall coefficient and explain how it is used to determine the type and concentration of charge carriers in a semiconductor. [5]

(b) Distinguish between Type I and Type II superconductors and state the Meissner effect. [3]