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First Semester End Term Examination : November, 2009

Applied Physics – I (Fields and Waves)

Time : 3 Hrs.

Maximum Marks : 70

Note: Values of Physical constants are given at the end of paper.

SECTION –A                                               (30 Marks)

Attempt any 5 questions.

Each question carries 6 marks.

1. (a) What is effect of damping on the natural frequency of an oscillator?

(b) Prove that when damping forces are present, the frequency of an oscillator is reduced by 12.5 /Q2, where Q is quality factor.

2. (a) If Φ is a scaler. Prove that curl grad Φ = 0.

(b) Prove that div curl of a vector is equal to zero.

3. (a) What is pointing vector? Explain.

(b) Write down Maxwell’s equation explaining each term.

4.  (a) Derive differential equation of wave motion.

(b) Compare the characteristics of the progressive and stationary waves.

5.  (a) Describe a method to determine the wavelength and velocity of ultrasonic waves.

(b) State the Gauss divergence theorem for electromagnetism.

6.  (a) Define specific rotation.

(b) A sugar solution in a tube of length 20 cm produces optical rotation of 130. The solution is than diluted to one third of its previous concentration. Find the optical rotation produced by 30 cm long tube containing the diluted solution.

SECTION –B                                               (20 Marks)

7.  (a) Derive an expression for the intensity distribution due to Fraunhofer diffraction at a single slit and show that the intensity of first order maxima is about 4.5% of that of the principle maxima.

(b) In Newton’s rings arrangement, the diameter of 10th dark ring changes from 1.5 cm to 1.27 cm when a liquid is introduced between the lens and glass plate. Calculate refractive index of liquid.

8.  (a) What do you understand by double refraction? Explain how would you use the phenomena to produce plane polarized light and circularly polarized light?

(b) How many orders will be visible if the wavelength of the incident radiation is 5000 Å and the numbers of lines on the grating is 2620 in one inch.

9.  (a) Explain the concept of Maxwell’s displacement current and show how it led to the modification of Ampere’s law.

(b) If the magnitude of magnetic field in a plane wave is 1 A/m, find the magnitude of electric field for plane wave in free space.

SECTION –C                                               (20 Marks)

10.  (a) Show that at the frequency of velocity resonance the absorption in a driven harmonic oscillator is maximum.

(b) For a uniformly charged solid sphere of charge density Ρ, calculate the electric field intensity at a point

(a) outside the surface,

(b) on the surface of the sphere.

(c) In biprism experiment, the distance between the slit and screen is 160 cm. The biprism is 40 cm away from the slit and its refractive index is 1.52. When a source of wavelength 5893 Å is used the fringes width is found to be 0.01 cm. Find the angle of prism.

(d) Fringes are produced with monochromatic light of wavelength 5800 Å. A thin plate of glass of refractive index 1.5 is kept in the path of one of the interfering beams and the central bright band from centre. Calculate the thickness of glass plate.