Short Answer TypeDraw a block diagram of a detector for AM signal and show, using necessary processes and the waveforms, how the original message signal is detected from the input AM waves.
With what considerations in view, a photodiode is fabricated? State it’s working with the help of a suitable diagram.
Even though the current in the forward bias is known to be more than in the reverse bias, yet the photodiode works in reverse bias. What is the reason?Draw a circuit diagram of a transistor amplifier in CE configuration.
Define the terms:Answer the following questions:
(a) In a double slit experiment using light of wavelength 600 nm, the angular width of the fringe formed on a distant screen is 0.1°. Find the spacing between the two slits.
(b) Light of wavelength 5000 Å propagating in air gets partly reflected from the surface of water. How will the wavelengths and frequencies of the reflected and refracted light be affected?
Long Answer TypeA group of students while coming from the school noticed a box marked “Danger H.T. 2200 V” at a substation in the main street. They did not understand the utility of such a high voltage, while they argued; the supply was only 220 V. They asked their teacher this question the next day. The teacher thought it to be an important question and therefore explained to the whole class.
Answer the following questions:
(i) What device is used to bring the high voltage down to low voltage of a.c. current and what is the principle of its working?
(ii) Is it possible to use this device for bringing down the high dc voltage to the low voltage? Explain.
iii) Write the values displayed by the students and the teacher.
(a) State Ampere’s circuital law. Use this law to obtain the expression for the magnetic field inside an air cored toroid of average radius ‘r’, having ‘n’ turns per unit length and carrying a steady current I.
(b) An observer to the left of a solenoid of N turns each of cross section area ‘A’ observes that a steady current I in it flows in the clockwise direction. Depict the magnetic field lines due to the solenoid specifying its polarity and show that it acts as a bar magnet of magnetic moment m = NIA. 
Ampere’s Law states that the line integral of magnetic field 
around any closed path in vacuum is μo times the total current through the closed path.
That is, 
Toroid is a hollow circular ring on which a wire of large number of turns is closely wound.
Let’s consider an air-cored toroid with center O. 
We have, 
which is the magnetic field due to a toroid carrying current.
b) Given, current is flowing in the clockwise direction for an observer who is on the left side of the solenoid. Implies, left face of the solenoid is the South Pole and right face acts as the North Pole. The magnetic field lines are directed from south to north, inside the bar magnet. Hence, the magnetic field lines are directed from left to right in the solenoid. The figure below illustrates the direction of flow of current inside the solenoid. 
Magnetic moment of single current carrying loop = IA
Therefore,
Magnetic moment due to the whole solenoid is, m = N(IA)
Where,
N is the number of turns of solenoid,
I is the current flowing through the loop, and
A is the area of the loop.
(a) Define mutual inductance and write its S.I. units.
(b) Derive an expression for the mutual inductance of two long co-axial solenoids of same length wound one over the other.
(c) In an experiment, two coils C1 and C2 are placed close to each other. Find out the expression for the emf induced in the coil C1 due to a change in the current through the coil C2.
(a) An electric dipole of dipole moment p⃗ consists of point charges +q and –q separated by a distance 2a apart. Deduce the expression for the electric field E⃗ due to the dipole at a distance x from the center of the dipole on its axial line in terms of the dipole moment p⃗. Hence show that in the limit x >> a, E⃗ → 2 p⃗/ (4p ε0 x3).
(b) Given the electric field in the region E⃗ = 2x i, find the net electric flux through the cube and the charge enclosed by it.
(a) Explain, using suitable diagrams, the difference in the behaviour of a
(i) conductor and
(ii) dielectric in the presence of external electric field. Define the terms polarization of a dielectric and write its relation with susceptibility.
(b) A thin metallic spherical shell of radius R carries a charge Q on its surface. A point charge Q/2 is placed at its centre C and another charge +2Q is placed outside the shell at a distance x from the centre as shown in the figure. Find
(i) the force on the charge at the centre of shell and at the point A,
(ii) the electric flux through the shell.
(a) Using Huygens’s construction of secondary wavelets explain how a diffraction pattern is obtained on a screen due to a narrow slit on which a monochromatic beam of light is incident normally.
(b) Show that the angular width of the first diffraction fringe is half that of the central fringe.
(c) Explain why the maxima at 
become weaker and weaker with increasing n.
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