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Physics 30
Electromagnetic Theory
Worksheet 1: Magnetism
equations describing the strength of magnetic fields?
1) What is believed to be the cause of all magnetic phenomena?
Andre Ampere
Moving charged particles produce a magnetic field. In
ferromagnetic materials, it is the unpaired spins of electrons
aligned in the same direction.
8) What was Faraday’s contribution to the study of
electromagnetism?
2) What is a magnetic domain?
A magnetic domain is an area in a ferromagnetic material in
which the magnetic dipoles of atoms are all aligned in the
same direction. The domain is said to be saturated with
dipoles.
3) A magnet attracts one end of an iron bar and repels one
end of a nickel bar. Further tests are made with these ends of
the two bars. Explain why the following conclusions may or
may not be justified.
a) The nickel bar is a magnet.
Yes, repulsion is a sign that the nickel bar is a pole of like
orientation
b) The iron bar is definitely a magnet
No, the iron bar could simply be ferromagnetic and it would
be attracted
c) The iron bar may be a magnet
Yes, the magnet could be acting on a pole of opposite
orientation.
d) The iron bar may be unmagnetized
Yes, the iron bar could simply be ferromagnetic and it would
be attracted
e) The nickel bar will attract the iron bar
Yes, since the nickel is a magnet, it should attract the iron bar
whether it is a magnet or just ferromagnetic.
Faraday developed the motor principle in which electrical current
can be converted into mechanical energy and the generator
principle in which mechanical energy can produce electrical
potential.
9) Who was Maxwell, and why was his contribution to
electromagnetism so significant?
James Clerk Maxwell was the developer of the first comprehensive
mathematical treatment of electromagnetism. He synthesized
the work of Oersted, Faraday and his own conception of
interacting electromagnetic fields to produce the four principles
which form the classical wave conception of electromagnetism.
10) What was Langevin’s contribution to the study of magnetism?
Langevin is noted for his work on paramagnetism and
diamagnetism and devised the modern interpretation
of this phenomenon in terms of spins of electrons within atoms.
11) What two types of motion within the atom contribute largely
toward the magnetic properties of atoms? Which is these is
more critical in explaining ferromagnetic properties?
1) The motion of electrons around the nucleus and 2) the motion
of electrons spinning on their axis. The more important to
ferromagnetic properties is the spin of electrons on their own
axis.
4) What is believed to be the major cause of the earth's
magnetism?
12) a) What is magnetic flux? State the properties of a flux line.
b) What is the definition of a magnetic field?
It is thought that the liquid iron core of the earth is subjected to
convection currents. The iron in this state is a charged plasma.
Magnetic flux (Greek letter Φ) is a measure of the
magnetic field strength existing on a two dimensional surface,
such as one side of a magnet. In textbook diagrams, magnetic
flux is usually pictured as cluster of vectors attached to a
geometrically abstract surface.
5) What type of magnetic pole exists in northern Canada?
The geographic north has a magnetic south pole.
The discovery demonstrated that electricity and magnetism, two
previously separate fields of study in Physics were related.
1) run from N to S outside the magnet
2) are closed curves (run south to north inside)
3) flux lines do not cross
4) flux lines repel one another
5) concentration indicates the flux density(in Teslas)
6) follow the path of least resistance
7) tend to shorten
7) Who developed the left hand rules and formalized mathematical
A magnetic field is the area of magnetic force around a substance
6) What was significant of Oersted’s discovery that magnetic
fields surround current carrying wires?
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Physics 30
Electromagnetic Theory
They can be caused by electric charge, by electric fields that
vary in time and by elementary particles that possess their own
'intrinsic' magnetic field, a relativistic effect which is usually
modeled as a spin of the particle.
18) Name two elements other than iron which are strongly
attracted by a magnet
13) State three ways to demagnetize a magnet.
19) What are the advantages of making a magnetic in a horseshoe
shape?
1) Dropping
2) Heating
3) Removing from a source of alternating current.
Two other ferromagnetic elements are nickel and cobalt.
14) What happens to the domains of an non-magnetized
ferromagnetic object when it is placed in a magnetic field?
The domains oriented in the same direction grow and the domains
oriented in different directions will shrink.
The horseshoe shape decreases the distance between the poles
of the magnet and therefore concentrates the magnetic flux lines
between the poles just on the basis of its shape.
15) If each of two N poles is doubled in strength, and at the same
time the distance between them is made half as great, what
change occurs in the force between them?
20. Define each of the following: a) declination b) dip
c) permeability d) retentivity e) domain.
Using ratio techniques and the concept that F = km1m2
mag
2
R
in a manner analogous to gravitational and electric fields, the
magnetic force would be 16x as great.
16) How large is the region of influence of a magnet?
a) The angle between the magnetic pole and the geographic
north pole.
b) The angle between the horizontal and the magnetic field
inclination to the ground.
c) The rate of magnetization of a material in response to a
magnetic field.
d) The degree to which a substance retains its magnetism after
a magnetizing field is removed.
The magnetic field theoretically extends to infinity.
Worksheet 2: Magnetic Fields for Current Carrying Wires
17) Three identical bar magnets are placed so that one pole of
each lies on the circumference of a circle of radius 10 cm. The
magnets are oriented as shown in the diagram below.
1) Calculate the magnetic field 9.0 cm from a long straight
conductor carrying a current of 3.0 A. (6.7 x 10-6 T)
μ 0I
2πR
2 x 107 (3.0)
β=
(.09)
β=
β = 6.7 x 10 6 T
State the approximate direction in which the north end of a
small magnetic compass needle would point, if its pivot
coincided with the center of the circle. Explain your answer.
2) Calculate the current in a long straight conductor if it
produces a magnetic field of 2.6 x 10-5 T at a distance of
25 cm from the conductor. (33 A)
I=
like poles repel and unlike poles attract.
The vector sum of the repulsions and attractions of the north
pole of the compass is shown above.
β2πR
μ0
(2.6 x 105 )(0.25)
I=
2 x 107
I = 33 A
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Physics 30
Electromagnetic Theory
3) A 25.0 cm solenoid has 1800 loops and a length of
25.02 cm. Calculate the magnetic field in the air core of the
solenoid when a current of 1.25 A is flowing. (1.13 x 10-2 T)
 = μ 0 In
6) Two long fixed parallel wires are 7.2 cm apart and carry
currents of 25 A and 15 A in the same direction. What is the
magnitude of the magnetic field midway between the two
wires? (5.6 x 10-5 T)
0 I
2 R
 = 4 (1 x 107 )(1.25)1800
1 =
 = 1.13 x 102 T
(2 x 107 )15
1 =
0.036
1 = 8.33 ... x 105 T
4) A circular coil with 190 loops of wire has a length of
3.40 cm. If the magnetic field at the center of this coil is
6.2 x 10-3 T, what is the current flowing through the coil?
(0.88 A)
I=

μ 0n
6.2 x 103
4 (1 x 107 )(190/.034)
I = 0.88 A
I=
5) An air core solenoid is 25 cm long and carries a current
of 0.72 A. If the magnetic field in the core is 2.1 x 10 -3 T,
how many turns does this solenoid have? (580)
n=
N=

μ 0I
L
μ 0I
2.1 x 103 (0.25)
N=
4 (1 x 107 ).72
N = 580 turns
 2 = 1.388... x 104 T
If the two currents are going in
the same direction, then the magnetic
fields between the wires will subtract
 net =  1 +  2
 net = 1.388... x 104 T + -8.33... x 105 T
 net = 5.6 x 105 T
7) The earth's magnetic flux density is approximately 3.0 x 10-5 T
At what distance from a long straight vertical wire carrying a
current of 8.0 A does the flux balance the earth's field? (5.3 cm)
R=
μ 0I
2π
2 x 107 (8.0)
3.0 x 105
R = 0.0533 m
R=
3
Physics 30
Electromagnetic Theory
8) A beam of 1.25 x 1010 e-/s leaves an accelerator with a speed
of 2.0 x 106 m/s. Calculate the magnetic flux density 4.0 cm from
the beam. (1.0 x 10-14 T)
e
1.6 x 1019 C
1.25 x 10
x
s
e
10) A current carrying wire has a magnetic field of
3.2 x 10-5 T at a distance of 3.0 cm from the wire. If the
current is tripled and the distance from the wire is reduced to
1.0 cm, what will the magnetic field strength be at this new
location? (2.88 x 10-4 T)
10
 2.0 x 109 A
μ 0I
2πR
2 x 107 (2.0 x 109 )
=
0.040
 = 1.0 x 1014 T
=
9) What is the magnetic field strength at the center of a loop of
wire:
a) 15.0 cm in diameter which is carrying a current of 17.5 A?
(1.47 x 10-4 T)
b) the same as in a, but with 300 loops/m.(4.40 x 10-2 T)
μ 0I
2R
2 x 107 (17.5)
=
0.075
 = 1.47 x 1014 T
a)  =
b)  = μ 0 In
 = 4 x 10 7 (17.5)300
 = 6.60 x 10 3 T
 new
 old
μ 0 3I
2(0.01)
=
μ 0I
2(0.03)
μ0 3 I
 new
2 (0.01)
=
 old
μ0 I
2 (0.03)
 new= 9 ( old )
 new= 9 (3.2 x 105 )
 new= 2.9 x 104 T
11) Two long fixed parallel wires are 8.00 cm apart and carry
currents of 15 A and 35 A in opposite directions. What is the
magnitude of the magnetic field midway between the two
wires? (2.5 x 10-4 T)
1 =
0 I
2 R
(2 x 107 )15
0.04
1 = 7.5 x 105 T
1 =
 2 = 1.75 x 104 T
If the two currents are going in
opposite directions, then the magnetic
fields between the wires will add
together.
 net =  1 +  2
 net =  7.5 x 105 T + 1.75 x 10 4 T
 net = 2.5 x 104 T
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Physics 30
Electromagnetic Theory
Worksheet 3: Motor Principle
1) A copper wire (L = 0.222 m) carries conventional current of
0.960 A north through magnetic field (= 7.50 x 10-4 T) that
is directed vertically upward. What is the magnitude and
direction of the magnetic force acting on the wire?
(1.60 x 10-4 N East)
RHR
thumb = current
fingers = magnetic field
palm = direction of magnetic force
Fmag =  IL
3) A wire in the armature of an electric motor is 2.50 x 10-1 m
long and is perpendicular to a magnetic field of 5.00 x 10-1 T.
Calculate the magnetic force on the wire when it carries a
current of 3.60 A. (4.50 x 10-1 N)
Fmag =  IL
Fmag = 5.00 x 101 (3.60)2.5 x 101
Fmag = 0.450 N
4) A current balance is used to determine the magnetic field
intensity in the core of a solenoid. The current balance and the
solenoid are described in the diagram. If the current balance is
balanced with a 2.3 x 10-5 kg mass, what is the magnetic field
strength in the solenoid core? (3.3 x 10-2 T)
Fmag = 7.5 x 104 (0.96)0.222
Fmag = 1.60 x 104 N
2) A solenoid lies in a horizontal plane with a current balance,
WXYZ, balanced horizontally in the solenoid core at points Z
and W as shown in the diagram. Sides WX and ZY of the
current balance conductor are 7.10 cm. Side YX is 1.90 cm. A
current of 6.00 A flows through the conductor on the current
balance. If a mass of 1.76 x 10-2 kg is necessary to balance the
current balance, what is the magnetic field strength in the
solenoid? (1.51T)
When the balance is in the balanced
position, the torques, and hence forces
(since the distances from the axis of
rotation are the same) are equal
Fmag = Fg
 IL = mg
When the balance is in the balanced
position, the torques, and hence forces
(since the distances from the axis of
rotation are the same) are equal
Fmag = Fg
 IL = mg
mg
IL
2.3 x 105 (9.81)
=
0.45(0.015)
 = 0.033 T
=
mg
IL
1.76 x 102 (9.81)
=
6.00(0.019)
 =1.51 T
=
5
Physics 30
Electromagnetic Theory
5) From the diagram below:
8) A rectangular loop is suspended by a spring scale between
magnetic poles. The loop is 0.060 m wide by 0.120 m high.
a) What kind of pole is at X?
b) Connect the ends of one dry cell to the ends of the coil
to produce the pole indicated in the diagram.
c) If a copper core were substituted for the iron, what
would happen to the strength of the pole at X?
a) X must be a south pole to attract the north of the compass.
b) To produce a south pole at X, the current would have to come
from the back to the front. The wire at the X end should be
connected to the negative terminal of a battery, and the wire on
the other end should be connected to the positive terminal.
c) Copper is not ferromagnetic. The iron bar down the center
produces a stronger magnetic because the domains align in the
direction of the magnetic field caused by the current. Copper will
therefore not produce as strong a magnetic field.
6) A bare current-carrying wire runs across a lecture table.
Describe at least two ways you could find the direction of the
current.
1) Use a compass – the compass will align in the direction of
the magnetic field when you place the compass at different
points around the wire. The pole from the wire can be used to
find the direction of the current using the left hand rule for
current carrying wires.
2) Bring a strong magnet close to the wire and tangent to an
imaginary circle around the wire. When the magnet repels the
wire, you will know that the two magnets are showing like
poles. The pole from the wire can be used to find the
direction of the current using the left hand rule for current
carrying wires.
7) An electron current-carrying wire is placed between the
poles of a magnet as shown at right. What is the direction of
the force on the wire?
Current in loop (A)
1.00
2.00
3.00
4.00
5.00
6.00
Total Force on Spring
1.5032
1.5063
1.5094
1.5128
1.5159
1.5225
a) What is the weight, in Newtons, of the loop?
b) What is the slope of the best fit line and what does it represent?
c) What is the magnitude of the magnetic field between the bar
magnets?
(1.50 N, 3.68 x 10-3 N/A increase in Fmag per ampere of current,
(6.13 x 10-2 T)
L1= Current (A)
L2= Total Force (N)
Note that in this case, the net force continues to get larger
and larger as the current increases, indicating that the magnetic
force in in the same direction as the gravitational force.
(out of the page towards you)
LHR
fingers = direction of magnetic field
thumb = direction of electric current
palm = direction of magnetic force
6
Physics 30
Electromagnetic Theory
9) An experiment is carried out to investigate the relationship
between the magnetic force F on a current-carrying wire in a
uniform magnetic field B and the current I in the wire. The
wire is placed in the plane of the page, as shown in the
diagram below. The direction of the magnetic field is
perpendicular to the plane of the page and directed into the
page.
(i) On the diagram above, draw a vector to indicate the
direction of the magnetic force on the wire when the current I
is in the direction shown.
LinReg(ax+b) L1,L2,Y1
a = 3.68 x 10-3 N/A
b = 1.50 N
r2 = 0.9770 …
LHR thumb = current , fingers = magnetic field, palm =
magnetic force
(ii) The current in the wire is decreased and the magnetic
force on the wire is measured.
(1) State the responding variable in this experiment.
The responding variable in this case would be the Fmag
min
max
scl
(2) Sketch a graph of the relationship between the two
variables.
Window x[ 0.5
6.5
0.5 ]
y[1.4999… 12.5257 … 0.005]
a) The weight of the loop is the Force when the current is zero,
or the y intercept of the graph = 1.50 N
b) The slope of the graph is the Force each additional amp of
current exerts on the bar. From the equation F mag = IL it will
also represent the magnetic field times the length of wire in
the magnetic field. Slope = 3.68 x 10-3 N/A
c) Since slope = Fmag /I = L
slope/L = 
 = 3.677 … x 10-3/0.060 = 6.13 x 10-2 T
(iii) Calculate the magnitude of the force per unit length that
acts on the wire if the current in the wire is 0.8 A. The
magnitude of the magnetic field B is 1.2 × 10-4 T.
7
Physics 30
Electromagnetic Theory
Fmag =  IL
Fmag
L
Fmag
L
= (1.2 x 104 )(0.80)
11) Two long parallel wires carry currents of 5.0 A and
7.5 A in opposite directions. If the force per meter on each
wire is 5.3 x 10-5 N, how far apart are the wires? (0.14 m)
μ 0 I1I 2
L
2πR
μ II
R= 0 1 2
2π(F/L)
Fmag
= 9.6 x 10
5
N/m
10) Explain, with reference to the diagram of a moving-coil
loudspeaker below, how the loudspeaker cone is set vibrating
by an oscillating current flowing through the voice coil.
=
2 x 107 (5.0)7.5
5.3 x 105
R = 0.14 m
R=
12) When a steady electric current of 10.0 A flows through the
circuit shown in the diagram, the parallel wires X and Y
attract each other with force of 5.00 x 10 -5 N.
If X and Y have equal resistance, calculate the force they would
exert on each other if the total current were increased to 20.0 A.
(2.00 x 10-4 N)
LHR
fingers = direction of magnetic field
thumb = direction of electric current
palm = direction of magnetic force
When the current goes into the page on the top coil, it will
come out of the page on the bottom coil and vice versa. Using
the left hand rule for the motor effect, the top and bottom will
both pull in on the speaker cone when the current is as
described. When the current reverses, the two interactions
will both push the speaker cone out. This will produce sound
waves of the same frequency as the current reversals in the
coil.
Fmag(new)
L
Fmag(old)
L
Fmag(new)
L
Fmag(new)
L
Fmag(new)
L
μ 0 (20)(20)
2πR
=
μ 0 (10)(10)
2πR
F
= 4 mag(old)
L
= 4 (5.00 x 105 )
= 2.00 x 104 N
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Physics 30
Electromagnetic Theory
13) Two straight, parallel wires 8.0 m long and 0.50 m apart
carry currents of 20 A in opposite directions.
a) What is the magnetic flux density at a point P midway between
the wires? (3.2 x 10-5 T)
I
1 = 0
2 R
(2 x 107 )20
0.25
1 = 1.6 x 105 T
1 =
 2 = 1.6 x 105 T
If the two currents are going in
opposite directions, then the magnetic
fields between the wires will add
together.
14) Two parallel wires are each 1.0 m long and 1.0 cm apart. If
one of the wires carries a current of 10 A and the magnetic force
between them is 1.0 x 10-4 N, what is the current in the second
wire? (0.50 A)
μ 0 I1I 2
L
2πR
Fmag 2πR
I2 =
μ 0 I1L
Fmag
=
1 x 104 (0.01)
2 x 107 (10)(1.0)
I 2 = 0.50 A
I2 =
15) The diagram shows an armature loop located between the
poles of a permanent magnet.
In a sentence, describe the direction of the rotation of the armature
loop according to the polarity of the armature, the permanent
magnets, and when viewed in the direction of the arrow.
 net =  1 +  2
 net = 1.6 x 105 + 1.6 x 10 5 T
 net = 3.2 x 105 T
b) What is the magnitude of the force exerted on each wire?
(2.6 x 10-3 N)
The electric current would flow upward in the wire on the right
and downward in the wire on the left.
μ 0 I1I 2
L
2πR
μ II
Fmag = 0 1 2 L
2πR
2 x 107 (20)20
Fmag =
x 8.0
0.25
Fmag = 2.6 x 103 N
LHR fingers = magnetic field thumb = electric current
palm = motor force.
Fmag
=
The left hand rule shows that the wire on the right will be
pushed out and the wire on the left will be pushed in by the
motor force. Viewed from below, the loop would turn
counterclockwise.
c) If the currents are in the same direction, what is the magnetic
flux density at P? (0 T)
If the currents are in opposite directions, then the magnetic fields
between the two wires will be going in opposite directions, and
at the midpoint would be equal strengths. Hence the fields would
sum to zero.
9
Physics 30
Electromagnetic Theory
16) i) The diagram shows a coil ABCD of wire carrying a
clockwise electric current I in a magnetic field directed to the right.
In the space below, give the direction of the force acting on each
side of the coil:
AB = no force as the magnetic field of the top wire is
perpendicular to the field magnet, so they do not interact.
BC = using LHR, the motor force on BC will be into the page.
CD= no force as the magnetic field of the top wire is
perpendicular to the field magnet, so they do not interact.
DA = using LHR, the motor force on DA will be out of the page.
ii) The diagram shows the same coil in a magnetic field directed
into the page. On the diagram, at
right, show the direction
of the forces acting on each side
of the coil.
Top wire = by left hand rule, will be pushed to the bottom of the
page but this will not cause turning around the axis.
Left side wire = by left hand rule will be pushed to the right side
of the page, but this will not cause turning around the axis.
Bottom wire = by left hand rule, will be pushed to the top of the
page but this will not cause turning around the axis.
Right side wire = by left hand rule will be pushed to the left side
of the page, but this will not cause turning around the axis.
Label the diagram showing:
• The commutator.
• The brushes.
• The position of the north and south poles of a magnet which
would produce the field shown.
• The direction in which the coil will commence to rotate if it
is initially stationary. (counterclockwise)
17) A small motor has a rotating loop consisting of 300 turns
of wire in a rectangle whose ends are 6.00 cm and whose sides
are 12.0 cm. The armature draws 4.00 A of current while the
long sides of the loop are across a field whose flux density is
0.120 T. What is the torque on the armature? (1.04 N .m)
 = N AI
 = (300)0.120(.06 x .12)4
 = 1.04 N m
18) A rectangular coil ABCD of dimensions 8·0 cm by 4·0 cm
is made up of 250 turns of wire. It is placed in a uniform
magnetic field with a flux density of 0·50 T. It is free to rotate
about an axis, PQ, as shown in the diagrams below. A current
of 9·0 mA flows through the coil.
a) Draw a diagram, from above, showing the angle of the coil
in the field when the torque is maximal.
(iii) If the coil is initially stationary, will the magnetic forces in the
diagram, at left above, cause it to move?
Yes, by the left hand rule for motor effect, the right wire will be
pushed into the page, and the left wire will be pushed out of the
page, causing turning around the central axis.
(iv) A simple DC motor is constructed as shown in the diagram
above.
A coil is free to rotate about the
axis of rotation in a magnetic field
directed to the right in the diagram.
b) The coil is then rotated 180° around axis PQ from the position
of maximum torque. Compare the torque in this position with
that described in part (a).
The torque will again be maximal.
10
Physics 30
Electromagnetic Theory
c) What is the magnitude of the maximum torque?
 = N AI
 = (250)0.50(.08 x .04)9 x 103
c) Calculate the torque on the coil when the plane of the coil is
at an angle of 35° to the magnetic flux as shown below. (The
view shown is from above – Hint: find where the torque would
be maximal)
 = 3.6 x 103 N m
d) What is the magnitude of the force on side BC of the coil
when the torque is maximum? ( 4.5 x 10-2 N)
Fmag =  IL(N)
Fmag = 0.50(9 x 103 )0.04(250)
 = N AIsin 35o (perpendicular to  )
Fmag = 4.5 x 102 N
 = (140)0.80(.22 x .15)3.0sin 35o
 = 6.36 N m
19) Two large bar magnets and a vertical coil are shown in the
diagram. The coil, ABCD, is able to rotate about a vertical axle,
XY, through its centre. The coil consists of 140 turns of wire.
Current can flow into and out of the coil along wires attached to
the upper end of the axle. The coil is 22 cm high and 13 cm wide
The magnetic flux density between the poles of the magnets is
0.80 T.
d) If the magnets and the coil described above are used as the
basis for an electric motor, what should be added to allow the
coil to keep rotating in the same direction?
Split ring commutator
20) If you wanted to produce the world’s strongest electric motor,
explain how you would construct it.
The commutator should be large with many wraps of wire, a
very strong magnetic field and a large electric current.
a) Before the current in the coil is turned on, what is the flux
through the coil when the plane of the coil is parallel to the field?
21). A coil consists of ten turns of insulated copper wire. It
is placed between the poles of magnets as shown in the
diagram. These magnets may be assumed to create a
uniform magnetic field of flux density 0·15 T. A current of
2·0 A is passed through the coil in the direction shown.
 = A
 = 0.80(0.22 x 0.13)
 = 0.023 Wb
b) When a current of 3.0 A flows through the coil, calculate the
magnitude of the force on side AB of the coil. (74 N)
Fmag =  IL(N)
Fmag = 0.80(3.0)0.22(140)
Fmag = 74 N
a) Calculate the torque that acts on the coil when it is in the
position shown in the diagram. (4.5 x 10 -3 Nm)
 = N AI
 = (10)0.15(.03 x .05)2.0
 = 4.5 x 103 N m
b) With electric current going into the left hand of the coil,
in what direction will the coil start to turn as seen from
position Z? (clockwise)
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Physics 30
Electromagnetic Theory
c) A device is placed at Z to allow current to be supplied to the
coil so that the coil rotates continuously.
i) Name the device.
ii) Explain how it works.
22) The diagram shows a plan (view from above) of a simple
electric motor. ABDC represents a wire coil which is able to
rotate about the axis of rotation shown.
(a) On this diagram show
(i) The magnetic field between the poles of the magnet;
(ii) The direction of the electric current flowing in the
side AB of the coil.
through a magnetic field. What is the magnitude and
direction of the magnetic field? (1.6 T West)
27) Calculate the magnitude and the direction of the magnetic
force on an alpha particle travelling upward at a speed of
2.11 x 105 m/s through a magnetic field that is directed down.
(0)
28) An electron is accelerated from rest by a potential
difference of 1.70 x 103 V, and then enters a magnetic field
of 2.50 x 10-1 T moving perpendicular to it. What is the
magnitude of the magnetic force acting on the electron?
(9.77 x 10-13 N)
29) An electron is accelerated by a potential difference and
then travels perpendicular through a magnetic field of
7.20 x 10-1 T where it experiences a magnetic force of
4.1 x 10-13 N. Assuming this electron starts from rest, through
what potential difference is the electron accelerated?
(3.6 x 101 V)
30) Calculate the downward acceleration on an electron that is
travelling horizontally at a speed of 6.20 x 10 5 m/s
perpendicular to a horizontal magnetic field of
2.30 x 10-1 T. (2.50 x 1016 m/s2)
31) A proton travelling vertically at a speed of 2.10 x 10 5 m/s
through a horizontal magnetic field experiences a magnetic
force of 9.50 x 10-14 N. What is the magnitude of the magnetic
field? (2.83T)
(b) If the magnetic field has strength 1.0 T and a current of
5.0 A flows through each wire in the coil, what is the force
(magnitude and direction) on a single wire in side AB of the
coil? The sides of the coil (AB and CD) have length 0.20 m
each.
(c) State why the arrangement as shown could not work as a
practical motor and describe briefly the modifications which
must be made in order that the motor can turn freely.
23) Calculate the magnitude and the direction of the magnetic
force on an electron travelling north at a speed of
3.52 x 105 m/s through a vertically upward magnetic field of
2.80 x 10-1 T. (1.58 x 10-14 N West)
24) Calculate the magnitude and the direction of the magnetic
force on an alpha particle travelling south at a speed of
7.40 x 104 m/s through a vertically upward magnetic field of
5.50 T.(1.30 x 10-13 N West)
25) Calculate the magnitude and the direction of the magnetic
field that produces a magnetic force of 1.70 x 10-14 N East on a
proton that is travelling 1.90 x 104 m/s North through the
magnetic field. (5.59 T up)
26) An electron experiences an upward force of
7.1 x 10-14 N when it is travelling 2.7 x 105 m/s south
32) Calculate the downward acceleration on a proton that is
moving horizontally at a speed of 7.50 x 105 m/s perpendicular
to a horizontal magnetic field of 2.70 x 10-1 T.
(1.94 x 1013 m/s2)
33) Ions travelling at a velocity of 3.50 x 107 m/s pass
undeflected through the velocity selector in a mass
spectrometer. If the magnetic field strength in the velocity
selector is 0.500 T, what is the electric field strength in the
velocity selector? (1.75 x 107 N/C)
34) A velocity selector is composed of a uniform magnetic
field ( = 4.00 x 10-2 T) and a uniform electric field
perpendicular to each other. If the electric field is produced by
using parallel plates that are 1.50 cm apart, what is the
potential difference between the plates that will permit singly
charged ions of speed 4.20 x 106 m/s to pass undeflected
through the selector? (2.52 x 103 V)
35) Singly charged ions pass undeflected through the velocity
selector of a mass spectrometer. This velocity selector has a
magnetic field ( = 2.50 x 10-1 T) and an electric field
(|E| = 7.00 x 103 V/m) perpendicular to each other. These ions
now enter the separation region where the magnetic field is the
same as in the velocity selector. If the radius of the deflected
ions is 8.12 x 10-3 m, what is the mass of each ion?
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Electromagnetic Theory
(1.16 x 10-26 kg)
36) A singly charged 7-Li ion (mass = 1.16 x 10-26 kg) is
accelerated from rest through a potential difference of
4.00 x 104 V. This ion then enters a magnetic field
( = 0.700 T) perpendicular to it. What is the radius of the
deflected ion? (1.09 x 10-1 m)
37) An ion source contains two isotopes of magnesium
(24-Mg, 25-Mg). These ions travel undeflected through the
velocity selector ( = 0.850 T, |E| = 4.60 x 105 V/m) of a mass
spectrometer. If both isotopes are singly charged, how far
apart are the lines on the ion detector? (Assume the magnetic
field strength in the ion separator is 0.250 T.) (0.045 m)
38) A singly charged carbon ion travels in a circular path
(R = 11.3 cm) through the ion separation region of a mass
spectrometer. If the velocity selector is composed of an
electric field (|E| = 7.50 x 104 N/C) and a magnetic field
(= 0.300 T) perpendicular to each other, what is the mass
number of the carbon isotope? (Assume that the ion separation
region also has a magnetic field of 0.300 T) (13)
39) In a mass spectrometer, a velocity selector allows singly
charged carbon-14 ions with a velocity of 1.00 x 106 m/s to
travel undeflected through the selector. If these ions enter the
ion separation region ( = 0.900 T), what is the radius of the
ions' path? (0.163 m)
1.4
1.7
2.6
3.2
3.7
1.2
1.5
2.4
2.8
3.3
a) Draw a graph plotting radius as a function of momentum
b) Using a suitable averaging technique, determine the
magnetic field used in the spectrometer. (0.69 ± 0.01 T)
44) What are the Van Allen belts and why do they ‘lift’ at night?
45) The Earth's magnetic field in space is stronger near the poles
than over the equator. At what location would the circular paths
followed by the charged particles around the magnetic field lines
have larger radii? Explain.
46) The Earth is under continual bombardment from energetic,
charged particles. The magnetic field of the Earth influences
the path of these particles. Draw a diagram and explain the
different paths these particles take as they approach the Earth’s
magnetic field at the equator or towards the poles.
47) A beam of electrons traveling at 1.8 x 10 8 m/s is directed
towards a 0.014 T magnetic field as shown in the diagram at
left below.
40) In a mass spectrometer it is found that the radius of the
path for singly charged 20-Ne ions is 15.1 cm in the ion
separation region. What would be the radius of the path for
singly charged 16-0 ions, assuming identical velocities in the
same mass spectrometer? (12.1 cm)
41) A beam of Pb2+ ions (mass = 3.44 x 10-25 kg) travel
through the velocity selector of a mass spectrometer at a
velocity of 5.00 x 104 m/s. What magnetic field strength is
required in the ion separation region to cause these ions to
travel in a circular path with a radius of 19.6 cm?
(0.274 T)
42) Doubly charged neon atoms are accelerated from rest
through a potential difference of 2.00 x 103 V. They then enter
a perpendicular magnetic field ( = 0.200 T) and move in a
circular path with a radius of 10.2 cm. What is the mass of the
neon ion? (3.33 x 10-26 kg)
43) A student using a mass spectrometer with a constant
magnetic field studied the relationship between the radius of
the circular path of a number of singly charged isotopes and
their momentum. The following data was determined:
(a = 9.0 x 1018 m/Ns b = -1.6 x 10-3 m  = 0.69 T)
Momentum
Radius
(x 10-20 kg•m/s)
(x 10-1 m)
0.83
0.74
a) Which of the diagrams, at right above, illustrates the path
of the electron beam once in the magnetic field? (Circle one.)
b) What is the radius of the path of the electron beam while
in the magnetic field? (0.073 m)
48) During periods in which the sun is particularly active (as it
was in the year 2001), explosions on the sun's surface can
result in high-energy protons and electrons leaving the sun
and striking the earth some time later
(a) (i) If the protons have speed 6.0 x 107 m/s and the earth
is 1.5 x 1011 m from the sun, how long does it take
for the protons to reach the earth? (2.5 x 103 s)
(ii) What would be the radius of the circular path taken
by these protons if they enter a region in which the earth's
magnetic field has a value of 5.0 x 10-8 T, and the protons
travel perpendicular to the field lines? (1.3 x 107 m)
(b) The charged particles are deflected by the earth's magnetic
field towards the earth's poles where they excite oxygen atoms
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Physics 30
Electromagnetic Theory
(among others) in the upper atmosphere. The oxygen atoms
then emit red and green light that can be seen in the sky as the
'auroras'. The diagram shows the relevant energy levels within
the oxygen atom and the electronic transition responsible for
the red light. What is the wavelength of the red light?
( Use E = hc/where h is Planck’s constant) (6.25 x 10-7 m)
circuit? (3.0 V)
4) A wire 50 cm long is at rest along the +x axis. A large magnet
generating a uniform field directed along the +y direction, of
magnitude 0.2 T, is moved in the +z direction with a speed of
30 m/s. Find the magnitude and direction of the EMF induced
in the wire. (3 V in the +x direction)
5) A metal bar 8.0 cm long is dropped crosswise through
a magnetic field whose flux density is 1.5 x 10-2 T.
a) What is the EMF between its ends if it passes through the
field at a velocity of 4.0 m/s? (4.8 x 10-3 V)
b) How fast must a 30. cm bar drop through the field in the
prior problem to produce an EMF of 12 V? (2.7 x 103 m/s)
(c) The ions bombarding the atmosphere can set up electric
currents in the earth's upper atmosphere (the 'ionosphere').
Assume that the current is very thin as if flowing in a wire.
(i) The current is 100 km above the earth's surface and has
value 5.00 x 106A. At a point on the earth's surface directly
beneath the current, what is the magnitude of the magnetic field
strength produced by this current? (1.00 x 10 -5 T)
(ii) If the current runs from south to north, what is the direction
of the magnetic field in part (i)? (East)
6) A wire, 20.0 m long, moves at 4.0 m/s perpendicularly
through a 0.50 T magnetic field. What EMF is induced in the
wire? (40 V)
7) In the figure below, assume that L is 0.10 m long and B is
5.0 T.
Worksheet 4: Electromagnetic Induction
(Ohms law V = IR where R is resistance in ohms)
1) A conducting rod 0.35 m long moves perpendicular to a
magnetic field (= 0.75 T) at a speed of 1.5 m/s. Calculate the
induced voltage in the rod. (0.39 V)
2) The line MN in the diagram shown below represents a straight
conductor 0.20 m long which is perpendicular to a magnetic field
of induction 5.0 T. Calculate the magnitude of the E.M.F., which
is generated when the conductor moves vertically into the paper,
so that it cuts through the field with a constant velocity into the
paper, of 10 m/s. (10 V)
3) Part of a closed circuit consists of a straight wire 1.5 m long
moving at a speed of 2.0 m/s perpendicular to a magnetic field
of 10 000 G (104 Gauss = 1T). What is the EMF induced in the
a) Calculate the induced EMF when L is moving at 10.0 cm/s
to the left (0.050 V)
b) State three ways of increasing the EMF generated in a).
c) If the induced current is 0.500 A, what force is needed to move
L at 10.0 cm/s (0.25 N)
d) Where does the energy come from to maintain this current?
e) If the electrical resistance of the rectangular circuit is increased,
how would the power required to maintain the same current
change?
f) In which direction do electrons move in wire L of the rectangular circ
right?
8) The conducting rod in the diagram below is 22.0 cm long,
and is moving at a speed of 1.25 m/s perpendicular to a 0.150
T magnetic field. If the resistance in the circuit is 2.25 , what
is the magnitude and direction of the current (electron flow)
through the circuit? (1.83 x 10-2 A clockwise)
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Physics 30
Electromagnetic Theory
Assume that the north pole of a magnet has been inserted into
the coil shown.
9) The conducting rod in the diagram below is 15 cm long,
and is moving at a speed of 0.95 m/s perpendicular to the
magnetic field.
If the resistance in the circuit is 1.5 , and a current of
5.6 x 10-2 A is induced in the circuit,
a) what is the magnitude of the magnetic field? (0.59 T)
b) what is the direction of the induced current (electron
flow)? (clockwise)
2) Many sensitive chemical balances are fitted with a magnetic
damper. Instead of the pointer swinging almost endlessly, it
comes to rest quickly. (See diagram) The damper is merely a
strip of aluminum attached to the pointer, which passes between
the magnet the jaws of a strong permanent magnet when the
pointer swings. Explain why this simple arrangement reduces
the speed of the pointer's movements.
3) In the diagram below, coil P is set oscillating so that it passes
up and down over the end of a magnet. Coil Q begins to move
also. Explain why this happens.
10) The conducting rod in the diagram below is 30.0 cm long
perpendicular to a 0.950 T magnetic field. .If the resistance in
the circuit is 3.25 what force is required to move the rod at a
constant 1.50 m/s? (3.75 x 10.-2 N)
11) A plane with a wing span of 6.25 m is flying horizontally
at a speed of 95.0 m/s. If the vertical component of the earth's
magnetic field is 4.70 x 10-6 T, what is the induced voltage
between the tips of the wings? (2.79 x 10-3 V)
4) When a bar magnet moves toward the copper ring electrons
flow as shown below
12) A rectangular coil of wire containing 5 loops is moved
at a speed of 2.7 m/s perpendicular to a 1.1 T magnetic field as
shown below. If the length of the side of the coil moving
perpendicular to the field is 0.18 m, and the resistance in the
circuit is 3.5 ,
a) what is the induced current? (0.76 A)
b) what is the direction of the current (electron flow)?
(counterclockwise)
What kind of pole is X? Explain.
b) When the magnet is alternately moved away from and
toward the ring at a given rate without touching it, the ring
will begin to move back and forth about the suspended strings
as if it were a pendulum. Explain.
c) If instead of copper the ring is made of nichrome (the mass
remaining the same - nichrome is the resistance wire found in
toasters) the ring will
move back and forth with
smaller
amplitude. Explain
Worksheet 5: Lens’s Law
1) Explain how you can determine the direction of an induced
E.M.F. (as viewed from above) with the use of Lenz's law.
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Physics 30
Electromagnetic Theory
8) (i) What is does Lenz's Law state about the direction of an
induced current?
(ii) A bar magnet moves downwards into a conducting coil as shown in
flow in the coil.
On the diagram sketch:
5) The arrows show the direction of the winding not the current
direction
• The lines of magnetic force around the bar magnet.
• The lines of magnetic force produced by the induced current in
the coil.
• The direction of the induced current in the coil and external
circuit.
Be sure to label clearly your additions to the diagram.
Two coils, A and B are connected as shown in the diagram. A
magnet is pushed into coil A. Describe the subsequent motion
of the magnet which is suspended by a light spring in coil B.
6) Electron flow is increasing in coil A in the figure below. In
which direction will a current be induced in coil B? If the current
were decreasing in A, what would be the direction?
(iii) What would happen to the direction and magnitude of the
induced current as the bar magnet fell through the coil and
emerged from the bottom of the coil? Explain your answer.
A reasonable sketch graph of current against time should be
included.
Worksheet 6: Generators and Motors
7) The magnet is pushed completely through the loop of the
figure below. What changes take place both in the direction and
magnitude of the induced current in the loop?
1) What is the difference between a generator and a motor?
2) The diagram shows a simplified electric motor circuit.
On the diagram and using arrows, show the direction of the
current in the coils and each side of the armature loop as well
as the direction that each side of the armature loop is moving.
3) An electric motor in a hair drier is running at normal speed
and, thus, is drawing a relatively small current. What happens
to the current drawn by the motor if the shaft is prevented
from turning, so the back EMF is suddenly reduced to zero?
Remembering that the wire in the coil of the motor has some
resistance, what happens to the temperature of the coil? Justify
your answers.
16
Physics 30
Electromagnetic Theory
4) The diagram below shows in outline an AC electric
generator. When a force (due to a jet of high velocity water or
high velocity steam for example) is applied to the turbine, both
the turbine and coil spin between the poles of a strong magnet
in an anticlockwise direction.
above arrangement so as to obtain such a DC motor. Draw a
diagram to illustrate your answer in the space opposite.
Worksheet 7: Maxwell and Hertz
1) List four principles that Maxwell used to formulate his
theory of electromagnetic radiation.
2) Suppose that the electric field of an electromagnetic wave
decreases in magnitude. Does the magnetic field increase,
decrease, or remain the same? Account for your answer.
3) What are the characteristics of electromagnetic waves? Do
they behave differently than other waves? Explain.
4) Television antennas normally have the receiver antennas in
a vertical position. From that, what can you deduce about the
directions of the electric fields in television signals?
(a) Explain why an electromotive force is generated in a
conducting wire which moves through a magnetic field.
5) Why must an alternating current dipole be used to generate
electromagnetic waves? What would happen if a direct current
source were used?
(b) On the diagram above indicate the direction of the
magnetic field line between the magnets; and the direction of
the induced EMF (if any) in each section of the rotating coil
(for the instant of time shown on the diagram).
6) The diagram shows a representation of the apparatus used
by Hertz to detect electromagnetic waves.
(c) Water strikes the turbine, turning the generator and causing
a current to flow in the external circuit. Explain how the
principal of conservation of energy applies to this series of
events.
5 )The diagram shows a simple electric generator in which a
coil of wire rotates inside a strong magnetic field.)
Describe how you might determine:
a) whether the waves are polarized.
b) the wavelength of the waves
c) the velocity of the waves
(i) With labeled arrows, indicate the following on the diagram:
- the direction of the magnetic field in the region of the coil
- the direction of the (conventional) current flowing in the
external circuit.
(ii) Is the current produced by this generator alternating or direct?
Explain your answer.
(iii) At the position of the coil shown in the diagram, is the value
of the current at a maximum or is it zero? Explain.
(iv) A direct current electric motor also contains a wire coil, which
rotates in a magnetic field. Explain how you would modify the
7) What are the causes of each of the following type of
electromagnetic wave:
i) radio
ii) microwave
iii) infrared light
iv) visible light
iv) x-rays
v) gamma rays
8) What happens to each of the following as the wavelength of
electromagnetic radiation gets shorter:
i) penetrating power
ii) energy
iii) wavelength
iv) frequency
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Physics 30
Electromagnetic Theory
9) What wavelengths of EMR are called ionizing radiation?
What does this term mean?
10) What types of EMR are capable of passing through the
earth’s atmosphere from outer space?
18