Calculate the polarisation vector molecularatomic

Question

Part -1:

Please follow the above format strictly to facilitate evaluation and to avoid delay.

1) Use only foolscap size writing paper (but not of very thin variety) for writing your answers.

2) Leave 4 cm margin on the left, top and bottom of your answer sheet.

3) Your answers should be precise.

4) While solving problems, clearly indicate the question number along with the part being solved. Be precise. Write units at each step of your calculations as done in the text because marks will be deducted for such mistakes. Take care of significant digits in your work. Recheck your work before submitting it.

5) This assignment will remain valid from January 1, 2017 to December 31, 2017. However, you are advised to submit it within 12 weeks of receiving this booklet to accomplish its purpose as a teaching-tool.

Question 1. a) Consider the figure given below. Charges q₁, q₂ and q₃ are placed at A, B and C, respectively, and q₁ = q₂ = -q₃ = 2μC. Determine the magnitude and the direction of the electric field at point P.

b) A 100 m long thread carries charges uniformly distributed along its length. An electron, 10 cm away from the centre of the thread along a line perpendicular to the thread experiences an attractive force of 2.7 × 10^-12N. Calculate the total charge on the thread.

c) What do you understand by electrostatic potential energy? Calculate the electrostatic potential energy for the system of charges shown below. Take q = 4µC and a = 2 cm.

Question 2. a) The capacitance of a parallel plate capacitor is increased by a factor of 5 when a dielectric material fills the space between its plates. What is the relative permitivity of the dielectric material? If this material is placed in between the plates of a cylindrical capacitor of outer and inner radii 12 cm and 10 cm respectively, calculate the capacitance per unit length of the cylindrical capacitor.

b) A glass of relative permittivity 4 is kept in an external electric field of magnitude 10²Vm^-1.

Calculate the polarisation vector, molecular/atomic polarisability and the refractive index of the glass.

Question 3. a) A copper wire of diameter 1 mm and length 30 m is connected across a battery of 2V. Calculate the current density in the wire and drift velocity of the electrons. The resistivity of copper is 1.72 x 10^-8 Ωm and n = 8.0 x 10²⁸ electrons m^-3.

b) A 10 eV electron is circulating in a plane at right angles to a uniform magnetic field of 1.0 × 10^-4 T. Calculate the orbital radius of the electron, cyclotron frequency, period of revolution, and the direction of circular motion of the electron as viewed by an observer looking along the magnetic field.

c) How do we differentiate between diamagnetic and paramagnetic materials? Show that for diamagnetic atoms placed in an external magnetic field B, the change in dipole moment is opposite to the direction of B.

d) Establish the relation B = μ₀ (H + M) for a ferromagnetic material.

Question 4. a) An electric generator comprises a square wire loop of side 100 cm. The loop has 50 turns and is placed in a magnetic field of 0.5T. By what frequency should this loop be rotated in the magnetic field to produce an AC voltage of peak value 250 V?

b) Explain the physical significance of the Maxwell's equation ∇xΒ = μ₀ ( J + ε₀∂E/∂t).

Derive the wave equation for the z-component of the electric field of an electromagnetic wave.

c) A sinusoidal plane electromagnetic wave propagates from water (n_w =1.33) to glass (n_g = 1.5). Calculate the reflection and transmission coefficients for this wave at the interface of the two media. Show that when an electromagnetic wave enters from one dielectric medium to the other, its frequency remains unchanged.

Part -2:

Question 1. a) The sodium lamp used in a physics laboratory gives out light uniformly. Suppose that the lamp uses 40 W. Calculate the magnitude of electric field.

b) Describe polarisation of light by reflection. How does degree of polarisation vary with angle of incidence of light?

c) Discuss the concept of missing orders with reference to double slit diffraction pattern.

d) Depict spatial evolution of Fresnel diffraction pattern.

Question 2. a) Obtain expressions for reflection and transmission amplitude coefficients when electric vector associated with a plane monochromatic electromagnetic wave is in the plane of incidence.

b) Obtain an expression for elliptically polarised light resulting due to superposition of two orthogonal linearly polarised light waves. Show that plane polarised light and circularly polarised light are special cases of elliptically polarised light.

Question 3. a) Obtain the expression for shift in fringes when a thin transparent sheet is introduced in the path of one of the waves in a double slit interference experiment.

b) A plano-convex lens of radius 1.0 m is placed on an optically flat glass plate and is illuminated by an extended monochromatic source. Assume that the point of contact is perfect. The diameters of the 10th and 5th dark rings in the reflected light are 4.50 × 10^-3m and 3.36 × 10^-3m. Next, the space between the lens and the glass plate 3 is filled with a liquid. The diameter of the 5th ring changes to 3.0×10 m.

Calculate the refractive index of the liquid when the ring is (i) dark, and (ii) bright, if the wavelength of light is 589 nm.

Question 4. a) A plane light wave of wavelength 580 nm falls on a long narrow slit of width 0.5 mm.

(i) Calculate the angles of diffraction for the first two minima. (ii) How are these angles influenced if the width of slit is changed to 0.2 mm?

(iii) If a convex lens of focal length 0.15 m is now placed after the slit, calculate the separation between the second minima on either side of the central maximum.

b) Discuss Rayleigh's criterion for resolving power of an optical instrument. Obtain an expression for resolving power of a microscope.

Question 5. a) An atomic system consisting of two energy levels, with population of higher energy level less than that of the lower level, is in thermal equilibrium. Show that the absorption of radiation dominates stimulated emission if radiation of appropriate frequency is introduced into the system. Comment on the consequences of this fact for laser action.

b) Two energy levels of an atomic system are separated by energy corresponding to frequency 3.0 × 10¹⁴ Hz. Assume that all atoms are in one or the other of these two energy levels, compute the fraction of atoms in the upper energy level at temperature 400 K. Take k_B = 1.38×10-²³J -1 and h = 6.6×10^-34Js.

c) The refractive indices of the core and cladding materials of an optical fibre are 1.51 and 1.39 respectively. Calculate the numerical aperture and light gathering capacity of the fibre.

Part -3:

Question 1. State, with reasons, whether the following statements are True or False.

i) Ideal voltage source has infinite internal resistance.

ii) Transformer is a passive device hence it cannot increase the voltage.

iii) Field effect transistor (FET) is a current controlled device.

iv) Forward biasing of a semiconductor junction diode reduces its energy band gap.

v) Amplifier with common collector mode offers maximum voltage gain.

vi) Ripple factor of a center tapped full wave rectifier is greater than that of a bridge rectifier, which uses four diodes.

vii) Operational amplifier in non-inverting mode cannot amplify negative signals.

viii) IC LM380 is a small signal amplifier used to amplify the voltage.

ix) Largest decimal number represented by a 2-digit hex number is 99.

x) In a CRO sweep generator output is given to the vertical deflection plates.

Question 2. a) Use superposition principle to find the current flowing through R2 in Fig.1. (6) Fig. 1

b) Explain with a neat diagram application of p-n junction diode as a peak voltage detector.

Question 3. a) A series LCR circuit with L = 400 mH, C = 20 nF and R = 250 ? is connected to an AC source of 65 V.

Calculate the resonance frequency and Q of the circuit. What is the current flowing through the circuit and voltage across the capacitor at resonance frequency?

b) Which processes are responsible for the charge carrier transport in a semiconductor? Which of these govern in the case of a bulk semiconductor when no potential is applied?

Question 4. a) Refer to the universal bias shown in Fig. 4.11 of your study material. If Vcc = 10V, R₁ = R₂ = R_C = R_E = 10kΩ, V_BE = 0.7V and β = 100, calculate V_B, V_E, I_E, I_B, V_C and V_CE.

b) h-parameters of a single stage CE amplifier are given as h_ie = 1 kΩ , h_re = 3 × 10^-4, h_fe = 60 and h_oe = 25 μA/V. Calculate A_i, A_v and Z_out with r_s =100Ω and r_L =10kΩ.

Question 5. a) State the Barkhausen criterion for sustained oscillation. Explain the operation of Colpitt Oscillator. For a Colpitt oscillator with 10 MHz frequency determine the equivalent capacitance, C forming tank circuit with 0.1 mH inductor.

b) In a voltage regulator circuit, the output voltage under no load condition is 12V while under full load it is 11.8V. Over the full range of input voltage variation the nominal voltage output of 12V varies by 50 mV. Calculate percentage line and load regulation.

Question 6. a) Draw a circuit of a non-inverting amplifier with gain 1 using op-amp. Draw the output voltage curve of this circuit for a step input of 5V amplitude and 50 kHz frequency, if the slew rate of the op-amp is 0.5 V/μs. (Use proper scale on the time axis to illustrate the effect of slew rate).

b) Design and draw the circuit of a three channel op-amp adder with channel gains of -5, -10 and -15 respectively.

Question 7. a) Draw a circuit of amplifier of gain 50 using IC 380. Use the non-inverting terminal as input signal terminal.

b) Design and draw the circuit of a regulated power supply using LM 317 to provide 30V output.

Question 8. a) Design and draw the circuit diagram of a Mod-6 ripple counter.

b) A 4-bit DAC produces 22 mV output for a digital input of 1011. What is the resolution for this DAC? Find out Vout for 0101.

Question 9. a) Explain the working of D-flip flop. How does it differ from a D-latch?

b) Explain the construction and working of a differential amplifier type EVM.