PHYS 241
CHUKA
UNIVERSITY
UNIVERSITY EXAMINATIONS
SECOND YEARS EXAMINATION FOR THE AWARD OF DEGREE OF BACHELOR
OF SCIENCE (PHYSICS, MATHS,COMPUTER SCIENCE) AND BACHELOR OF
EDUCATION (SCIENCE)
PHYS 241: ELECTRICITY AND MAGNETISM 1
STREAMS: BSC(PHYS, MATH, COMP SC, APPLIED COMP SC, BED(ARTS)
TIME: 2
HOURS
DAY/DATE: THURSDAY 06/12/2018
11.30 A.M – 1.30 P.M
INSTRUCTIONS
Answer Question ONE and ANY Other TWO Questions.
Important information: µo = 4π x10-7 H/m), ɛo = 8.854 x 10-12 F.m−1, electron mass = 9 ×
10-31 kg, electron/proton charge = 1.6 × 10–19 C
Question One (30 marks)
(a) A current of 3.18 mA flows through a conductor of electricity in 4 minutes. Calculate the
amount of charge flowing through the conductor during this time.
(3marks)
(b) Four charges, q1 = 3.79 µC, q2 = 4.21 µC, q3 = 9.17 µC and q4 = 17.13 µC are placed as
shown in figure 1.1. If the distance between q1 and q2 is 30 cm, that between q1 and q3 is 20
cm while that between q1 and q4 is 40 cm. Calculate the electrostatic force experienced by q1
due to q2, q3 and q4
(3marks)
Figure 1.1. Four charges placed at four corners of a parallelogram.
(c) A current carrying wire loop and solenoid were design by a first year student in Chuka
University. Sketch the wire loop and solenoid showing the magnetic flux configuration.
(3marks).
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PHYS 241
(d) Two positive point charges were placed close to each other as shown in figure 1.2. Sketch the
electric field due to these point charges.
(2marks)
Figure 1.2. Two positive point charges.
(e) A charge of 60 µC is flowing through a magnetic field of 1.5 Teslas at a velocity of 300 m/s.
Calculate the magnetic force experience by the charge?
(3marks)
(f) The potential difference between two points along a conductor of electricity is 4.67V. What is
its resistance if the current flowing through the conductor is 0.683 A?
(3marks).
(g) Mains electricity is generated at the power station by a technique known as electromagnetic
induction. State three factors that determined the magnitude of induce emf in the coil.
(3marks)
(h) Two point charges, q1 = 53 µC and q2 = 103 µC are separated by a distance of 19 cm as
shown in figure 1.3. Calculate the total electric field at point P, 17 cm from q2.
(3marks)
Figure 1.3. Two point charges separated by a distance of 19 cm
(i) Three capacitors of 3.45 µF, 2.63 µF and 6.79 µF were connected in series within an electric
circuit. What is the total resulting capacitance?
(3marks)
(j) Using the superposition theorem, determine the current I1 for the network in figure 1.4.
(4marks)
Figure 1.4. Two-source network to be analyzed using the superposition theorem
Question two (20 marks)
(a) Using Biot-Savart law, show that the expression for magnetic flux due to a long wire at a
single point, a distance x from the wire is given by;
B=
μI
0
2 πx
where B is the magnetic flux, x is the distance from the wire at which magnetic field is to be
determined while µo is the permeability of free space
(10marks)
(b) A step up transformer has 100 and 100000 primary and secondary turns respectively. If the
Page 2 of 5
PHYS 241
input voltage is 240 V.
(i) What will be the output voltage?
(3marks)
(ii) Describe four ways to minimize power wastage in this transformer.
(4marks)
(c) A 250 µF capacitor was charged to a voltage of 12 V. determined the energy stored in this
capacitor
(3marks)
Question three (20 marks)
(a) Two parallel wires carry currents of 8 A and 2A in the same direction as shown in figure 3.1.
(i) What is the magnitude of the magnetic field midway between the wires? (6marks)
(ii) What is the direction of the net magnetic field?
(1mark)
(iii) Where between the two wires is the magnetic field zero?
(5marks)
(iv) How much magnetic force is experience by wire 2 due to the current in wire 1?
(2marks)
Figure 3.1. Two parallel wire carrying currents of different magnitude.
(b) The electrical circuit in figure 3.2 was used to study Thévenin theorem. It has resistors and a
voltage source.
Figure 3.2. Volatge source connected to the resistor network.
Calculate Thévenin equivalent circuit for the network in the shaded area of the network in
figure
3.2.
(5marks)
Question four (20 marks)
(a) A simple potentiometer with three terminals can be designed with two resistors and used as a
voltage divider in a circuit as shown in figure 4.1. A is input, B is output and C is the ground.
Page 3 of 5
PHYS 241
Figure 4.1. Two resistors connected to form a potentiometer for pd measurement.
Calculate the fixed voltages that can be obtained from its output terminal and how to connect
them to the required electrical component
(4marks)
7
(b) An electron moving in a circular orbit in an atom at a speed of 3 ×10 m/s experienced a
magnetic field of 6 × 10–4 T perpendicular to it.
(i) What is the radius of the circular orbit
(2marks)
(ii) What is the frequency of the electron?
(2marks)
(iii) Calculate the energy of the electron in keV. (1 eV = 1.6 × 10–19 J)
(2marks)
(c) A group of three equal charges, Q are placed at the corners of an equilateral triangle of side a.
Show that the resultant force on the charge at the top of the apex of the triangle is given by;
2
F=
Q √3
4πε0 a2
(10marks)
where Q is the charge placed at each apex of the triangle, a is the length of the side of the
triangle.
Question five (20 marks)
(a) Consider the arrangement of resistors shown in figure 5.1;
6Ω
5Ω
3Ω
2Ω
I qB
q7.1 1q12
q 1 qq51IW P C
W
62V resistor
Figure 5.1. A circuit
showing
network.
1
i
Ω
Ω
9
72i
1
43
1V 22
A
r
r
Determine the
= c
=e
e
(i)
equivalent resistance in the circuit c
(3marks)
m c
(ii)
current flowing in the circuit
(2marks)
m18
m
2
A
A
(iii)
current flowing through the 6 Ω resistor
(3marks)
(b) What's the force on a 0.5C charge moving at velocity v = (2i+5j+10k) ms-1 in a magnetic field
B = (8i+3j+5k) x 10-4 Teslas.
(2marks)
Page 4 of 5
PHYS 241
(c) A particle of mass m is rotating as it describes a circular path of radius R and experiencing
magnetic field of magnitude B. If the particle has a charge q, show that the period of rotation T is
T=
2 πm
qB
given by;
(3marks)
(d) Figure 5.2 shows a current source connected to a voltage source through a network of
resistors. Using the superposition theorem, determine the current through resistor R2 for the
network.
(7marks)
Figure 5.2. Current source connected to the resistor network and the voltage source.
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Page 5 of 5
CHUKA
UNIVERSITY
UNIVERSITY EXAMINATIONS
FIRST YEAR EXAMINATION FOR THE AWARD OF DEGREE OF BACHELOR OF
SCIENCE IN PHYSICS
PHYS 241: ELECTRICITY AND MAGNETSM
STREAMS: B.Sc COMPUTER, B.Sc APPLIED COMPUTER, B.Ed SCIENCE & BSC
PHYSICS
TIME: 2 HOURS
DAY/DATE: THURSDAY 7/12/2017
2.30 P.M - 4.30 P.M.
INSTRUCTIONS:
Speed of light =3.0×108 m/s
Εo =8.85×10-12 C2/N.m
1
𝐾 = 4𝜋𝜀 = 9𝑥109 𝑁𝑚2 𝑐 −2
0
e = 1.6𝑥10−19 𝐶
Answer question ONE which is compulsory and any other TWO questions
QUESTION ONE [30 MARKS]
a. Define the following terms
(i). Capacitor
(ii). Electric field
(iii). Electron Volt
(iv). Equipotential
[4 Marks]
b.A computer data acquisition card, inserted into the expansion slot in its motherboard has a
resistance of 300 Ω and operated by 240V power supply terminal. Calculate the current flowing
through it and explain use of the mother board.
[3 Marks]
ci).State Kirchoff’s laws
[2 Marks]
ii).Find the values of I1,I2 andI3 in the circuit below.
[5 Marks]
Page 1 of 6
d) A 8µC point charge is at the origin, and appoint charge of -3 µC is on the x axis at (6, 0) m as the
figure below. If the electric potential is taken to be zero at infinity, find the total electric potential
due to these charges at point p, with coordinates (0, 8) m.
[4 Marks]
P
3µ
C
e. Calculate the resistance per unit length of a 22-gauge nichrome wire of radius 0.28mm.Resistivity
of the wire is 1.5×10-6Ω.m . ii.If a potential of 16.0V is maintained across a 1.0m length of
nichrome wire. What is what is current in the wire?
[4 Marks]
8µ
C
f. A student makes circular coil of 800 loops of thin copper wire with a resistance of 0.25Ω. The
coil diameter is 14.0cm and the coil is connected to a 12.0V battery. Determine:
i).The magnetic moment of the coil
[3 Marks]
ii).The maximum torque on the coil if it were placed between the poles of a magnet where the
magnetic field strength was 1.8T.
[2 Marks]
g) What is the value of the unknown resistor R in if the voltage drop across
the 500 Ω resistor is 2.5 volts ? All resistances are in ohm.
Page 2 of 6
[3 Marks]
QUESTION TWO 20 MARKS
a). The circuit shown below consists of a 32mH inductor, a 4.0 Ω resistor, and a 12 V battery. The
switch is closed at t=0.Find the time constant of the circuit.
[2 Marks]
ii)Find the current after ONE time constant as elapsed it=63.2%
[2 Marks]
b) . Calculate the inductance of a solenoid containing 800 turns if the solenoid is 20cm and its cross
sectional area is 2cm2.
[3Marks]
c. An airplane with a wing span of 80m flies parallel to the earth’s surface at a location in which
the downward component of the Earth’s magnetic field is 2.80×10-3 T. Find the difference in
potential between the wing tips when the speed of the plane is 700m/s.
[3Marks]
d. A coil of 200 turns of wire is wrapped on a square frame 16cm on side. The total resistance of
the coil is 2 Ω. A uniform magnetic field is applied perpendicularly to the plane of the frame and
the field changes uniformly from 0 to 0.6T in 0.2s.Find the magnitude of the induced emf in the coil
while the field is changed.
[4 Marks]
e). Two resistors R1 and R2 may be connected either in series or parallel across a battery with emf
ε .We desire the thermal energy transfer rate for parallel combination to be five times that for the
series combination. If R1=100 Ω. What is R2?
[4 Marks]
f) An ideal 800W transformer has 50turns on its primary coil and 100 turns on its secondary coil. If
the primary coil is connected to a 120.0V source. What is the output voltage of the secondary coil?
[2 Marks]
QUESTION THREE 20 MARKS
a). Show that the magnetic field inside and outside a long straight wire carrying a current, I, is
directly proportional and inversely proportional to r respectively, where r is the distance from the
center of the wire.
[3 Marks]
b) How long does it take for 50% of the maximum charge to be deposited on the circuit below
when the switch is closed? The resistor is 4 million ohms and each capacitor is 20nF.
[4 Marks]
Page 3 of 6
c). A parallel plate capacitor has plates with dimensions 2cm ×4cm separated by 2mm.The plates
are connected across a 24 V battery. Determine the:
(i) Capacitance of the capacitor
[3 Marks]
(ii) Magnitude of the charge on each plate
[2 Marks]
d). Consider three point charges at the corners of triangle q1=8×10-9 ,q3=5×10-9,q2= -2×10-9
.Calculate resultant force at q3=50˚.
[4 Marks]
e) A proton moves at 4.0 x 106 m/s along the x axis. It enters a region where there is a magnetic
field of magnitude 7.5 T directed at an angle of 30° from the positive y-axis and lying in the xyplane. What is the initial force the proton feels and what is its acceleration?
[4 Marks]
QUESTION FOUR 20 MARKS
a) State Coulomb’s TWO laws for the electrostatics
[2 Marks]
b) What is the current through the battery and power provided in the circuit drawn below? (Neglect
the internal resistance and V= 18V).
[3 Marks]
Page 4 of 6
c) An electron and a proton are separated by a distance of 8.2 ×10-11m.Find theelectrostatic force
between them.
[3 Marks]
d) Show that the equivalent capacitance of capacitors 𝐶1 and 𝐶2 connected in series is
𝐶 𝐶
𝐶𝑒𝑞 = 𝐶 1+𝐶2 .
1
[3 Marks]
2
e) What is the equivalent resistance of this circuit? R1= 4Ω, R2= 8Ω, R3= 10Ω, R4= 20Ω
[4 Marks]
f) Calculate the expression for the electric potential difference at a point (P) a distance (Z) along
the axis of a uniform ring of radius (R) and total charge (Q). Discuss the limit z >>R.
[5 Marks]
QUESTION FIVE 20 MARKS
(a).
State:
i).Lenz’s law
ii).Faraday’s law of induction
iii).Back emf
[2 Marks]
[2 Marks]
[1 Mark]
b.i An electric heater is operated by applying a potential difference of 240V to a nichrome wire of
total resistance 12Ω.Find the current carried by the wire and the Power rating of the heater.
[3 Marks]
ii).If the heater is operated daily for 8hours how much will cost to pay electricity bill at the end 30
days. One kWh costs 12.40.
[2 Marks]
c)The charge Q of a capacitor decays according to the equation Q=Qoe-t/RC. If a fully charged
capacitor carries a charge of 9.2*10-3 C, what will be the amount of charge on the plates of the
capacitor after a period of time equal to the time constant.(use e=2.72)
[3 Marks]
d) Determine the capacitance of a single capacitor that is equivalent to the parallel
combination of capacitors shown below .Find voltage on the 12µF capacitor
32V
Page 5 of 6
[3Marks]
e) Suppose one wants to make a 0.25Ω resistor out of 2g of copper. If the resistor is a
uniform cylinder, what is the diameter and length required? Take the density of copper to be
8.95 x 103 Kg m-3. and resistivity to be 1.7𝑥10−8 𝛺. 𝑚
[4 Marks]
…………………………………………………………………………………………………………
Page 6 of 6
CHUKA UNIVERSITY
PHYS 241 : ELECTRICITY AND MAGNETSM
STREAMS: BSC COMPUTER, BSC APPLIED COMPUTER, Bed
PHYSICS
TIME: 2 HRS
SCIENCE & BSC
INSTRUCTIONS:
Speed of light =3.0×108 m/s
Εo =8.85×10-12 C2/N.m
𝐾=
e = 1.6𝑥10−19 𝐶
1
= 9𝑥109 𝑁𝑚2 𝑐 −2
4𝜋𝜀0
Answer question ONE which is compulsory and any other TWO questions
QUESTION ONE 30 MARKS
a. Define the following terms
(i). Capacitor
(ii). Electric field
(iii). Electron Volt
(iv). Equipotential
[4marks]
b.A computer data acquisition card, inserted into the expansion slot in its motherboard has a
resistance of 300 Ω and operated by 240V power supply terminal. Calculate the current flowing
through it and explain use of the mother board.
(3marks)
ci).State Kirchoff’s laws
(2marks)
ii).Find the values of I1,I2 andI3 in the circuit below.
(5marks)
e. A 8µC point charge is at the origin, and appoint charge of -3 µC is on the x axis at (6, 0) m as the
figure below. If the electric potential is taken to be zero at infinity, find the total electric potential
due to these charges at point p, with coordinates (0, 8) m.
(4marks)
P
3µ
C
e. Calculate the resistance per unit length of a 22-gauge nichrome wire of radius 0.28mm.Resistivity
of the wire is 1.5×10-6Ω.m . ii.If a potential of 16.0V is maintained across a 1.0m length of
nichrome wire. What is what is current in the wire?
( 4marks)
8µ
C
f. A student makes circular coil of 800 loops of thin copper wire with a resistance of 0.25Ω. The
coil diameter is 14.0cm and the coil is connected to a 12.0V battery. Determine:
i).The magnetic moment of the coil
(3marks)
ii).The maximum torque on the coil if it were placed between the poles of a magnet where the
magnetic field strength was 1.8T.
(2marks)
g) What is the value of the unknown resistor R in if the voltage drop across
the 500 Ω resistor is 2.5 volts ? All resistances are in ohm.
(3marks)
QUESTION TWO 20 MARKS
a). The circuit shown below consists of a 32mH inductor, a 4.0 Ω resistor, and a 12 V battery. The
switch is closed at t=0.Find the time constant of the circuit.
(2marks)
I
a
R
ε
b
S
ii)Find the current after ONE time constant as elapsed it=63.2%
(2marks)
b) . Calculate the inductance of a solenoid containing 800 turns if the solenoid is 20cm and its cross
sectional area is 2cm2.
(3marks)
c. An airplane with a wing span of 80m flies parallel to the earth’s surface at a location in which
the downward component of the Earth’s magnetic field is 2.80×10-3 T. Find the difference in
potential between the wing tips when the speed of the plane is 700m/s.
(3marks)
d. A coil of 200 turns of wire is wrapped on a square frame 16cm on side. The total resistance of
the coil is 2 Ω. A uniform magnetic field is applied perpendicularly to the plane of the frame and
the field changes uniformly from 0 to 0.6T in 0.2s.Find the magnitude of the induced emf in the coil
while the field is changed.
(4marks)
e). Two resistors R1 and R2 may be connected either in series or parallel across a battery with emf
ε .We desire the thermal energy transfer rate for parallel combination to be five times that for the
series combination. If R1=100 Ω. What is R2?
(4marks)
f) An ideal 800W transformer has 50turns on its primary coil and 100 turns on its secondary coil. If
the primary coil is connected to a 120.0V source. What is the output voltage of the secondary coil?
(2marks)
QUESTION THREE 20 MARKS
a). Show that the magnetic field inside and outside a long straight wire carrying a current, I, is
directly proportional and inversely proportional to r respectively, where r is the distance from the
center of the wire.
[3marks]
b) How long does it take for 50% of the maximum charge to be deposited on the circuit below
when the switch is closed? The resistor is 4 million ohms and each capacitor is 20nF.
(4marks)
c). A parallel plate capacitor has plates with dimensions 2cm ×4cm separated by 2mm.The plates
are connected across a 24 V battery. Determine the:
(i) Capacitance of the capacitor
(ii) Magnitude of the charge on each plate
(3marks)
(2marks)
d). Consider three point charges at the corners of triangle q1=8×10-9 ,q3=5×10-9,q2= -2×10-9
.calculate resultant force at q3.
(4marks)
8m
q2
-
6m
q1
+
+
q3
10m
x
e) A proton moves at 4.0 x 106 m/s along the x axis. It enters a region where there is a magnetic
field of magnitude 7.5 T directed at an angle of 30° from the positive y-axis and lying in the xyplane. What is the initial force the proton feels and what is its acceleration?
(4marks)
QUESTION FOUR 20 MARKS
a) State Coulomb’s TWO laws for the electrostatics
(2marks)
b) What is the current through the battery and power provided in the circuit drawn below? (Neglect
the internal resistance and V= 18V).
(3marks)
c) An electron and a proton are separated by a distance of 8.2 ×10-11m.Find theelectrostatic force
between them.
(3marks)d)
d) Show that the equivalent capacitance of capacitors 𝐶1 and 𝐶2 connected in series is
𝐶 𝐶
𝐶𝑒𝑞 = 𝐶 1+𝐶2 .
1
2
marks)
e) What is the equivalent resistance of this circuit? R1= 4Ω, R2= 8Ω, R3= 10Ω, R4= 20Ω
(3
(4 marks)
f) Calculate the expression for the electric potential difference at a point (P) a distance (Z) along
the axis of a uniform ring of radius (R) and total charge (Q). Discuss the limit z >>R. (5 marks)
QUESTION FIVE 20 MARKS
(a).
State:
i).Lenz’s law
(2marks)
ii).Faraday’s law of induction
(2marks)
iii).Back emf
(1mark)
b.i An electric heater is operated by applying a potential difference of 240V to a nichrome wire of
total resistance 12Ω.Find the current carried by the wire and the Power rating of the heater.
[3marks]
ii).If the heater is operated daily for 8hours how much will cost to pay electricity bill at the end 30
days. One kWh costs 12.40.
[2marks]
c)The charge Q of a capacitor decays according to the equation Q=Qoe-t/RC. If a fully charged
capacitor carries a charge of 9.2*10-3 C, what will be the amount of charge on the plates of the
capacitor after a period of time equal to the time constant.(use e=2.72)
(3marks)
d) Determine the capacitance of a single capacitor that is equivalent to the parallel
combination of capacitors shown below .Find voltage on the 12µF capacitor
6µF
12µF
18µF
24µF
32V
[3marks]
e) Suppose one wants to make a 0.25Ω resistor out of 2g of copper. If the resistor is a
uniform cylinder, what is the diameter and length required? Take the density of copper to be
8.95
x
(4 marks)
103
Kg
m-3.
and
resistivity
to
be
1.7𝑥10−8 𝛺. 𝑚