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Electromagnetic Theory Question Paper

Electromagnetic Theory

Course:Bachelor Of Education (Science)

Institution: Kabarak University question papers

Exam Year:2011

KABARAK
UNIVERSITY

UNIVERSITY EXAMINATIONS
2011/2012 ACADEMIC YEAR
FOR THE DEGREE OF BACHELOR OF EDUCATION SCIENCE

PHYS 323: ELECTROMAGNETIC THEORY
DAY: TUESDAY

DATE: 29/11/2011
TIME: 2.00 – 4.00 P.M.

STREAM: SESS VI
INSTRUCTIONS:
Answer question ONE and any TWO other questions.
Question ONE carries 40 marks while all the other questions carry 15 marks each.
You may use the following constants:
eo = 8.85 x 10-12 F/m; µo = 4px10-7Tm/A; c = 3.0 x 108 m/s; Zo = 377
Electron charge

e = 1.6 x 10-19C; Rest mass of an electron Me = 9.1 x 10-31kg
Rest mass of a proton
Mp = 1.672 x 10-27kg; Resistivity of copper
? = 1.7 x 10-8

QUESTION ONE (40 MARKS)
a) State any FOUR properties of electromagnetic waves

[2 mark]
a)
In some region of space the electric field and the magnetic field give equal contributions to the
energy density. Find the ratio of E to B.

[2 marks]
b)
Sunlight strikes earth with an average intensity of 1400W/m2. Find the peak electric and magnetic
fields.

[4 marks]
b) Describe briefly what you understand by eddy current. How can it be reduced?

[3 marks]
c) An electron in the ground state of the hydrogen atom has an orbital angular momentum of
1.05 x 10-34J·s. Find the orbital magnetic moment.

[2 marks]
d) A current of 5.00mA flows into a 10.0pF capacitor with circular plates of radius 2.00cm. Find
i)
The displacement current,

[1 mark]
ii)
the rate of change of the electric flux,

[2 marks]
iii)
the rate of change of electric field,

[3 marks]
iv)
the magnetic field 3.00cm from the center of the plates

[2 marks]
v)
The magnetic field 1.00cm from the center of the plates.

[2marks]
1

e) Define ‘pointing vector’

[1 mark]
f) State Lenz’s law

[1 mark]
g) The electric field Ey of a TransverseElectroMagnetic (TEM) wave equals 100Vm-1 rms. Find:
i)
velocity and pointing vector magnitude PV in air

[2 marks]
ii)
velocity and PV in a lossless dielectric medium with er = 9

[2 marks]
h) Study figure 1 below

Figure 1

From the figure, find:
i)
Voltage standing wave ratio(VSWR)

[2 marks]

ii)
Reflection coefficient ? for the wave of the figure

[2 marks]

i) A conducting rod of length l is free to slide on two parallel conducting bars as in Figure 2 below

Figure 2
In addition, two resistors R1 and R2 are connected across the ends of the bars. There is a uniform
magnetic field pointing into the page. Suppose an external agent pulls the bar to the left at a constant
speed. Evaluate the following quantities:
i)
The currents through both resistors;

[3 marks]
ii)
The total power delivered to the resistors;

[2 marks]
iii)
The applied force needed for the rod to maintain a constant velocity

[2 marks]

2

QUESTION TWO (15 MARKS)
a)
A solenoid (shown in figure 3) has 1000 turns of wire. It is 10.0cm long and 1.00cm in diameter.
Estimate the self inductance.

[5 marks]

Figure 3

b)
The inductor in a) above is made of copper. Find:
i)
Its resistance,

[5 marks]
ii)
The equilibrium current when it is connected to a 1.50V battery

[2 marks]
iii)
The time required for it to reach 99% of this equilibrium current.

[3 marks]

QUESTION THREE (15 MARKS)
a)
State and briefly explain THREE types of magnetic behaviour

[6 marks]
b)
A circular loop of wire of radius a is placed in a uniform magnetic field, with the plane of the loop
perpendicular to the direction of the field, as shown in Figure 4. The magnetic field varies with time
according to B = Bo+ bt where Bo and b are positive constants.

i)
Calculate the magnetic flux through the loop at t = 0

[3 marks]
ii)
Calculate the induced e.m.f in the loop.

[2 marks]
iii)
What is the induced current and its direction of flow if the
overall resistance of the loop is R?

[2 marks]
Figure 4
iv)
Find the power dissipated due to the resistance of the loop

[2 marks]

QUESTION FOUR (15 MARKS)
a)
Calculate the ocean depths at which a 1 Vm-1 field will be obtained with E at the surface equal to 1
Vm-1 at frequencies of 1, 10, 100, and 1000 kHz. What is the most suitable frequency for
communication by wireless with undersea craft? ( assume at the sea, s = 4 m-1, and er = 80)

[5 marks]
3

b)
Suppose a magnetic monopole is found experimentally. Fix Maxwell's Equations and find the SI
units of magnetic charge

[5 marks]
c)
Show that E = Em sin(kz - ?t) is a wave moving in the positive z direction. Express
k and w in terms of the wavelength, ?, and the frequency, f and find their relationship to the
velocity.

[5 marks]
4

Electromagnetic Theory Question Paper

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