PHY/VI/11 Student's Copy
2 0 1 8
6th Semester
PHYSICS
ELEVENTH PAPER
Electromagnetic Theory
Revised
Full Marks 55
Time 2½ hours
PART A—OBJECTIVE
Marks 20
The figures in the margin indicate full marks for the questions
SECTION—A
Marks 5
Tick the correct answer in the brackets provided 1×5=5
1. The energy density of a monochromatic plane wave travelling in vacuum is
(e0 permittivity of free space, E electric field)
e0
E2 2 0
e E2
4 0
e E2 8 0
e E2
2. The speed of an electromagnetic wave in a dielectric medium where m m0
and e 4e0 is speed of light in vacuum)
c
4
c
2

c 2c
3. An electric field
r
E in terms of scalar V and vector potential
4. Slew rate of an op-amp is a parameter that defines
how rapidly the output changes with the change in input
frequency
how rapidly the output changes with the change in operating
voltage
the rate at which mathematical operation is performed
the rate of change of output resistance
5. The decimal equivalent of (1001)2 is
7 8
9 10
SECTION—B
Marks 15
Answer the following questions 3×5=15
1. The electric field of an electromagnetic wave in vacuum is given by
whereE is in volts per meter, t is in seconds and x is in meters. Determine
the wavelength, direction of propagation of the wave and direction of the
magnetic field.
2. State and explain Brewster's law in electromagnetic waves.
3. Magnetic vector potential is given by
r
A x2i$ 2xy $j. Obtain the magnetic
field at 0).
4. What is output offset voltage of op-amp? Explain how it can be adjusted.
PHY/VI/11 2 Contd.
5. Draw the output waveform for the given input waveforms to a two-input
NAND gate
PART B—DESCRIPTIVE
Marks 35
The figures in the margin indicate full marks for the questions
1. Derive the Poynting theorem and obtain the expression for Poynting vector. 7
OR
Derive Maxwell's equation
D is electric displacement
and r is the charge density. 3
Using Maxwell's equations, discuss the boundary conditions for
magnetic field vector at the interface between different media. 4
2. Deduce the laws of refraction for plane waves at the boundary of two
dielectrics from electromagnetic theory. 5
A uniform plane wave whose electric field is given by
EI =100cos(wt 6px)z$ Vm-1 is incident from a region having e1 4e0,
m1 m0 normal to the plane surface of a material having e2 9e0,
m2 4m0. Obtain the expression for the reflected electric field. 2
OR
Obtain the expression for skin depth when electromagnetic wave is
incident on a conducting surface from air medium. 5
A 2 MHz electromagnetic wave propagates in a non-magnetic medium
having a relative permittivity of 2e0 and a conductivity of 100 S/m.
Determine if the material is a good conductor or not. Calculate the skin
depth. [e0
8 × 85 ´10-12 Fm-1 2
3. What do you mean by gauge transformations? Show that Lorentz condition
leads to two decoupled differential equations in electric field and magnetic
field.
OR
What are the scalar and vector potentials in electromagnetic waves? Derive
the Poisson's equation using vector potential with the current density. 7
4. Draw the circuit diagram of a basic differentiator using op-amp. Derive
the expression for its output voltage. Draw the output waveform for the
square wave given below 5
Write at least four characteristics of ideal op-amp. 2
OR
With the help of appropriate circuit diagram, explain the use of op-amp
as unity follower. Give at least one application of unity follower circuit. 3½
Explain CMRR of an op-amp. Give reason why high CMRR is suitable. 3½
5. Write the Boolean equation for the digital circuit shown below and give
its truth table 3
Simplify the Boolean expression Z × and realize its using
NAND gates.
Write the truth table and draw the digital circuit of half adder. 4
Using complement, perform binary subtraction of the following 3
(110011)2 (100111)2
(101×1101)2 (101× 0111)2