Applied Engineering Physics 2018 Question Paper — Government College…

Instructions

• Attempt five questions in all, selecting at least two questions from each section.
• Each question carries 20 marks.
• Use of scientific calculator is allowed.

Questions

Section A

• Q1. (a) Derive the equation of continuity $\nabla \cdot \vec{J} + \frac{\partial P}{\partial t} = 0$. How does it lead to the concept of displacement current ? Explain its significance in Maxwell's equations of electromagentism. Show that it has dimensions of conventional current. 12 (b) An electromagnetic wave propagates through a medium having relative permittivity 4 and relative permeability 1. Find the velocity of the wave. 8 [20 marks]
• Q2. (a) Explain the physical significance of a wave-function. Discuss the conditions and limitations, a wavefunction must obey. Derive time independent Schrödinger's wave equation and express it for a free particle also. 12 (b) Prove uncertainty relation for energy and time from position momentum uncertainty relation. 8 [20 marks]
• Q3. (a) Distinguish between free, damped and forced oscillations. Deduce the differential equation of a forced harmonic oscillator and find its solution. Discuss its different cases. 12 (b) Show that the ratio of the energy lost per cycle to the energy stored in the damped oscillator is $\frac{2\pi}{Q}$, where $Q$ is the quality factor. 8 [20 marks]
• Q4. (a) Explain what is meant by the divergence of a vector field $\vec{A}$. Derive expression for Div $\vec{A}$ in Cartesian co-ordinates. Discuss its physical significance. 12 (b) Find the probability that a particle trapped in a box of width 'L' can be found between 0.1 L and 0.2 L for the ground and the first excited states. 8 [20 marks]

Section B

• Q5. (a) Describe drift and diffusion currents and derive Einstein's relation for a P-N junction. 12 (b) The resistivity of a doped silicon material is $9 \times 10^{-3}\ \Omega\text{m}$. The Hall co-efficient is $3.6 \times 10^{-4}\ \text{m}^3/\text{C}$. Assume single carrier conduction, find the mobility and density of charge carriers. 8 [20 marks]
• Q6. (a) Differentiate between Fresnel and Fraunhofer's class of diffraction. Prove and explain the rectilinear propagation of light by using the concept of Fresnel's half period zones. 12 (b) Calculate the thickness of a doubly refracting crystal required to introduce a path difference of $\frac{\lambda}{2}$ between O and E rays when $\lambda = 6000\ \text{Å}$, $\mu_o = 1.65$ and $\mu_E = 1.48$. 8 [20 marks]
• Q7. (a) Differentiate between : (i) Laser and Ordinary light (ii) Holography and Photography Explain the principle of Holography. How is hologram produced and how is the image reconstructed from it. Discuss some of its applications. 12 (b) A glass clad fibre is made with core glass of refractive index 1.5 and the cladding is doped to give a fractional index difference of 0.0005. Find : (i) Cladding index and (ii) Numerical aperture. 8 [20 marks]
• Q8. (a) Obtain expressions for charge densities in $n$-type and $P$-type semiconductors. Give an expression for the mobility of a charge carrier. 10 (b) Describe the construction of a Nicol prism. Explain how it can be used as a polariser and as an analyzer. 10 [20 marks]

Related pages

• Applied Engineering Physics syllabus
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