Download PHE_07E (2003)

PHE-07
ASSIGNMENT BOOKLET
Bachelor's Degree Programme (B.Sc.)
ELECTRIC AND MAGNETIC PHENOMENA
School of Sciences
Indira Gandhi National Open University
Maidan Garhi,
New Delhi-110068
2003
Dear Student,
We hope you are familiar with the system of evaluation to be followed for the Bachelor’s Degree
Programme. At this stage you may probably like to re-read the section on assignments in the
Programme Guide for Elective Courses that we sent you after your enrolment. A weightage of 30 per
cent, as you are aware, has been earmarked for continuous evaluation which would consist of two
tutor-marked assignment for this course. TMA-1 is based on Blocks 1 and 2; TMA-2 is based on
Blocks 3 and 4.
Instructions for Formatting Your Assignments
Before attempting the assignment please read the following instructions carefully:
1) On top of the first page of your TMA answer sheet, please write the details exactly in the
following format:
ENROLMENT NO.:……………………………………………
NAME :……………………………………………
ADDRESS :……………………………………………
……………………………………………
……………………………………………
COURSE CODE:
…………………….
COURSE TITLE :
…………………….
ASSIGNMENT NO. ………………….…
STUDY CENTRE: ………………..…..
DATE : ….………………………………………...
PLEASE FOLLOW THE ABOVE FORMAT STRICTLY TO FACILITATE EVALUATION
AND TO AVOID DELAY.
2) Use only foolscap size writing paper (but not of very thin variety) for writing your answers.
3) Leave 4 cm margin on the left, top and bottom of your answer sheet.
4) Your answers should be precise.
5) 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.
6) This assignment will remain valid for one year. However, you are advised to submit it within 8
weeks of receiving this booklet to accomplish its purpose as a teaching-tool.
We strongly feel that you should retain a copy of your assignment response to avoid any unforeseen
situation.
We wish you good luck.
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Tutor Marked Assignment-1
Electric and Magnetic Phenomena
Course Code: PHE-07
Assignment Code: PHE-07/TMA-1/2003
Max. Marks: 100
Attempt all questions. The marks for each question are indicated against it. The symbols have
their usual meanings.
1. In each of the following questions we have given you four possible answers of which only one is
correct. Choose the correct alternative, giving reasons. Each question carries 3 marks.
a) It is not true that electric lines of force
i) leave positive charges and enter negative ones
ii) are close together where an electric field is strong and far apart where the field is weak
iii) have the same pattern around a charged sphere as they do around a point charge
iv) actually exist
b) Two charges of +Q are 1 cm apart. If one of the charges is replaced by a charge of –Q, the
magnitude of the force between them is
i) zero
ii) smaller
iii) the same
iv) larger
c) Ten million electrons are placed on a solid copper sphere. The electrons become
i) uniformly distributed on the sphere’s surface
ii) uniformly distributed in the sphere’s interior
iii) concentrated at the centre of the sphere
iv) concentrated at the bottom of the sphere
d) A system of two charges has a positive potential energy. This signifies that
i) both charges are positive
ii) both charges are negative
iii) both charges are positive or both are negative
iv) one charge is positive and the other is negative
e) The work to move a charge Q on a equipotential line for a distance r is
QV
i)
joules
4  o r 2
V
ii)
joules
r
iii) zero
iv) QVr joules
2. a) Give one example of each of the following:
i) charging by friction
ii) charging by induction
iii) charging by conduction
(53)
(13)
b) “Electrical force is about 1039 as strong as the gravitational force”. Cite an example which is
an exception to the statement (Hint: Unit 1 will help you in answering this question.)
(3)
c) “Volt” is the special name for the unit “Joules per coulomb”. When we say that the voltage
of a car battery is 12 V what do we mean by it?
(4)
3
3. State Gauss’s law. A very long cylinder of radius R has uniform charge density  C m3. Find the
magnitude and direction of the electric field E both inside the cylinder and outside the cylinder.
Plot E as a function of r, the distance from the axis of the cylinder.
(2+8)
4. a) What is the potential energy change when 2 coulombs of charge flow from one terminal of a
9V battery to the other through a radio?
(5)
b) Draw the electric field lines and equipotentials for a point charge. Also discuss their nature.
(2+3)
c) The electron in a hydrogen atom is at a distance of 0.53  1010 m from the proton. The
proton is a small ball of charge with q = e = 1.6  1019 C. What is the electrostatic potential
generated by the proton at this distance? What is the potential energy of the electron? (2+3)
5. Give short answers giving reason(s), wherever required.
(310)
a) Explain why some molecules possess a permanent dipole moment. Name two such
molecules.
b) How does inserting a dielectric in a parallel plate capacitor affect i) its capacitance, and
ii) potential difference across its plates. Explain.
c) A dielectric having dielectric constant 3 is inserted in a capacitor charged to 12.0 V. What
will the potential difference across the plates be after the dielectric is inserted between them?
d) Calculate the effective capacitance of the following combination of capacitors:
e) Calculate the charge on a 1000 F capacitor charged to a voltage of 1V.
f) What is the effective capacitance of a capacitor that has 6 plates connected in parallel? The
capacitance of each unit is 100 pF.
g) The distance between the plates of a parallel plate capacitor is 2.0 mm and the potential
difference between them is 10V. What is the electric field energy density for the capacitor?
h) Write the SI units of electric displacement vector, dielectric constant and atomic polarisability
using their definitions.
i)
Express relative permittivity of a solid in terms of its atomic/molecular polarisability.
j)
Explain why the relative permittivity of polar molecules varies with frequency.
4
6. a) What is the capacitance of a parallel plate capacitor that has square plates of dimensions
(100 mm  100 mm), plate separation of 0.25 mm and polystyrene between the plates? What
is the charge on it if the potential difference across it is 50 V? Calculate the energy stored in
it. The dielectric constant of polystyrene is 2.6.
(10)
b) Calculate the dielectric displacement D and the polarisation P for the parallel plate capacitor
of part (a) of this question.
(5)
c) Calculate the charge stored in a capacitor consisting of two concentric spheres of radii 50 cm
and 51 cm if the potential difference between them is 100 V. Assume the dielectric constant of
air to be 1.
(5)
5
Tutor Marked Assignment-2
Electric and Magnetic Phenomena
Course Code: PHE-07
Assignment Code: PHE-07/TMA-2/2003
Max. Marks: 100
Attempt all questions. The marks for each question are indicated against it. The symbols have
their usual meanings.
1.
.
In each of the following questions we have given you four possible answers of which only one is
correct. Choose the correct alternative, giving reasons. Each question carries 2 marks.
a) Inside a solenoid the magnetic field
i) is zero
ii) is uniform
iii) increases with distance from the axis
iv) decreases with distance from the axis
b) The magnetic field at a distance 2 cm from a long, straight wire is 106 T. The current in the
wire is
i) 0.01 A
ii) 0.1 A
iii) 1A
iv) 10A
c) An observer moves past a stationary electron. His instruments measure
i) an electric field only
ii) a magnetic field only
iii) both electric and magnetic fields
iv) any of the above, depending upon his speed.
d) All magnetic fields originate in
i) iron atoms
ii) permanent magnets
iii) magnetic domains
iv) moving electric charges
e) The magnetic field of a bar magnet most closely resembles the magnetic field of
i) a straight current carrying wire
ii) a stream of electrons moving parallel to one another
iii) a current carrying wire loop
iv) a horse shoe magnet
(25)
2.
(a)
(b)
(c)
In the above three situations I is the current flowing in the wire and +q is the charge. In (a) +q is
stationary, in (b) +q is moving with a velocity V and in (c) +q is circulating in a plane normal to
the current. In which of the cases the charge experiences a force. Give reasons.
(10)
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3. (a) A toroid of aluminium of length 1m, is closely wound by 100 turns of wire carrying a steady
current of 1A. The magnetic field B in the toriod is found to be 1.2567104 wbm2. Find H
and Km.
(4)
(b) In what way do the atoms, molecules or ions which constitute a paramagnetic material differ
from those which constitute a diamagnetic material.
(6)
4.
5.
Metallic iron contains approximately 1029 atoms per cubic meter. The magnetic moment of each
iron atom is 1.8  1023 Am1.
a)
If all the dipoles were perfectly aligned what would be the magnetisation M and the magnetic
moment of a bar 10 cm long and 1 cm2 in cross-section?
(5)
b)
What would be the torque on this ferromagnetic bar in a field of 102 Tesla perpendicular to
the axis of the bar?
(5)
a)
State whether the following statement is true or false. Give reasons.
 H.dl  i free implies that the field H is determined solely by real electric currents and is not
b)
c)
affected by the presence of magnetic materials.
(3)
In free space M = 0. Why?
(3)
 E.dl  0
d
 E.dl   dt  B.ds
(Eq.1)
(Eq.2)
Comment on E appearing in the above two equations in not more than two sentences.
6.
a)
Calculate the induced emf in a loop perpendicular to a spatially uniform magnetic field when
the magnitude of the field changes linearly
i) from 400 mT to 200 mT in 1.0 ms, and
ii) from 1.0 T to 1.4 T in 0.1 ms.
7.
(4)
(5)
b)
In the sliding wire circuit of Fig. 13.7 of Unit 13, a resistance of 2 k is used and it is given
that the length L = 500mm, magnetic field is 1.0 T and v = 1.5 ms1. Calculate the induced
emf and the induced current in the circuit.
(5)
a)
A solenoid of length 0.5 m is made by winding 500 turns of wire on an iron rod. The
cross- section of the rod is 5 cm2. What is the self-inductance of the solenoid, if the
relative permeability of iron is 600? What average emf is induced in the solenoid
as the current in it is decreased from 0.5 A to 0.1 A in a time of 0.1s?
(2½+2½)
b)
Two coils A and B having 5000 and 20,000 turns, respectively, are situated close to each
other so that their planes are parallel. A current of 1.0 A in A causes a flux of 0.9 × 102 Wb
through B. Determine (i) the mutual inductance of A and B and (ii) the average induced
emf in B when the current in A is switched off in 0.1s.
(2½+2½)
8. Show that the x component of the electric field of an electromagnetic wave in vacuum obeys the
three-dimensional wave equation with
1
.
speed c 
 0 0
Hint: Start from the differential form of Maxwell’s equations.
(10)
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9. a) The E field of an electromagnetic plane wave in vacuum is given by
 1012

E  ˆj 100sin  
z  10 20 t  Vm 1 .
 3



Determine the wavelength, frequency, direction of propagation and the magnitude and
direction of magnetic field of the wave.
(15)
b) The coefficient of reflection R and coefficient of transmission T are equal to 0.5 at normal
incidence on the interface between two dielectrics. Show that the ratio of the indexes of
refraction is 5.83.
(5)
10. A uniform plane wave of 100 MHz travelling in free space strikes a block of a dielectric for
which  = 4 0 ,  = 90 and  = 0, normal to the surface. The incident electric field vector is
given by
E  100 cos (t  y ) zˆ Vm 1
Write complete expressions for the incident, reflected and transmitted field vectors.
8
(10)