Applied Engineering Physics 2014 Question Paper — Government College…

Instructions

• Attempt Five questions, Selecting at least two questions from Section A and Two questions from Section B.
• All questions carry equal marks.

Questions

Section - A

• Q1. a) Show that curl of a vector Field which can be expressed as gradient of another scalar field vanishes i.e. if $\vec{A} = \vec{\nabla} \varphi$ then $\vec{\nabla} \times \vec{A} = 0$. b) Discuss the physical significance of divergence and curl of a vector. [20 marks]
• Q2. a) State and prove Gauss-divergence theorem. b) Show that $\vec{\nabla} \frac{1}{|\vec{r}|} = -\frac{\vec{r}}{|\vec{r}|^3}$. c) Evaluate divergence of $\vec{A}$ where $\vec{A} = -3\hat{i} + 2\hat{j} + 4\hat{k}$ [20 marks]
• Q3. a) Write down Maxwell's equation for steady and Varying electric and magnetic fields both in differential and integral forms and explain their physical significances b) State and derive the equation of continuity. [20 marks]
• Q4. a) Using Ampere's law find the magnetic field at a point due to a long solenoid. b) Derive wave equations for electric and magnetic fields in free space. Define and state the significance of poynting vector. [20 marks]

Section - B

• Q5. a) Discuss the theory of Newton's ring and determine the wavelength of monochromatic light by Newton's ring method. b) Describe the construction of a Nicol's prism. Explain how it can be used as a polarizer and analyzer. [20 marks]
• Q6. a) Describe Fraunhofer diffraction due to a single slit and deduce the position of the maxima and the minima. b) A soap film of refractive index $1.33$ is illuminated with light of different wavelengths at an angle of $45^\circ$ there is complete destructive interference for $\lambda = 5890 \mathring{A}$. Find the thickness of the film. [20 marks]
• Q7. a) Define forced oscillations. Deduce the differential equation of a forced harmonic oscillator and find its solution. b) What are ultrasonic waves? How they can be produced? Explain. [20 marks]
• Q8. a) Explain the construction and working of He-Ne laser. Draw the energy level diagram and indicate the wavelength of radiation. b) Calculate the acceptance angle and critical angle for an optical fibre whose core index is $1.48$ and cladding index is $1.39$. [20 marks]

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