MAGNETIC FIELDS AND ELECTROMAGNETIC EFFECTS

MAGNETIC FIELDS

- Magnetic field is a region around a magnet within which magnetic forces act.
- The direction of a magnetic field is the direction of a free north pole.
- This direction is represented using magnetic field lines

Magnetic
flux

Stronger
field

Weaker
field

Magnetic flux, ∅

- Magnetic flux refers to magnetic field lines combined together.

- It is measured in Weber, Wb.
- The closer the field lines (magnetic flux) are together, the stronger the field.

Magnetic flux density, B

- This is the measure of the strength of a magnetic field.

- It is the amount of flux per unit area.
- It is measured in Tesla (T)

magnetic flux,∅
magnetic flux density, B =
area

∅
B=
A

pg. 1
∅ = 𝐁𝐀
𝑊𝑒𝑏𝑒𝑟
𝑇𝑒𝑠𝑙𝑎 =
𝑚2

1 T = 1Wbm−2

- Depending on the flux density, a given area will have a certain quantity of flux.
- This value of flux is a measure of the total effect of the field on a magnetic substance.
- Maximum effect is achieved when the area is perpendicular to the flux direction.
- If the flux is at an angle 𝜃 to a given region/area, A, then flux is determined by
multiplying the area enclosed by the region by the component of the flux density
perpendicular to the area.
∅ = 𝐁𝐬𝐢𝐧 𝛉 𝐱 𝐀

Example 1

Consider figures (a) and (b) below:

(a) If the bar magnet in fig (a) causes a magnetic field with a flux density of 20mT
perpendicular to the plane of area A, how much flux will be contained in this area if
it is 10cm2?

Answer

∅ = BA

= 20 x 10−3 T x 10 x 10−4

pg. 2
= 2.0 x 10-5 Wb

(b) In fig (b) the uniform magnetic field has a flux density of 5 x 10-5 T and is at an angle
of 750 to the region of area, A. How much flux will be contained by this area if it is
1cm2?
Answer
∅ = Bsin θ x A
= 5 x 10−5 sin 75 x 1 x 10−4
= 4.8 x 10-9 Wb

Flux linkage

- The interaction between magnetic fields and charged particles or conductors, allows
motors to operate, and electricity to be generated.
- In most practical applications, magnetic flux is made to interact with a coil of wire, as
the effect on single strand of wire is too small to be useful.
- Therefore, as the magnetic field interacts with the coil, any effect is multiplied N
times, where N is the number of turns of the coil.
- The amount of magnetic flux interacting with a coil of wire is known as the flux
linkage.
𝐹𝑙𝑢𝑥 𝑙𝑖𝑛𝑘𝑎𝑔𝑒 = 𝑁∅ 𝑚𝑒𝑎𝑠𝑢𝑟𝑒𝑑 𝑖𝑛 𝑊𝑒𝑏𝑒𝑟
𝑟𝑒𝑐𝑎𝑙𝑙𝑖𝑛𝑔 𝑡ℎ𝑎𝑡 ∅ = 𝐵𝐴
𝐅𝐥𝐮𝐱 𝐥𝐢𝐧𝐤𝐚𝐠𝐞 = 𝐁𝐀𝐍

TASK
1. Vora takes a wire and winds it into a coil of ten circular turns with a radius of 5
cm and then holds this in a magnetic field with a strength of 20mT. What is the
flux linkage?
2. The Earth acts as a giant bar magnet, and the geographic North Pole is at the
magnetic South end of the field.

pg. 3
 (a) Draw a sketch of the Earth with its magnetic field
(b) Explain wher you would expect the Earth’s magnetic flux density to be
greatest.
3. In Britain, the Earth’s magnetic flux density is 50 000nT, with the field close to
horizontal. Imagine you are Britain.
(a) Estimate the flux passing through your body if you stand vertically and face
north.
(b) A typical smartphone compass uses magnetometer chip to determine which
way the phone is facing. Such chips are typically 2 mm by 2 mm squares. If
you held a smartphone o the magnetometer chip was at an angle of 200 to the
horizontal, what would be the flux passing through the chip for it to measure.
4. In an electric motor, a permanent magnet of flux density 18.4 mT has its field
placed perpendicular to a coil of 250 turns of copper wire. The diameter of the
coil is 8.50 cm. What is the flux linkage between the field and the coil?

FLEMMING’S LEFT HAND RULE

Magnetic field due to current carrying conductor

- A direct current has a magnetic field around it, which is produced by charging
particles in motion.

- The shape of the field is concentric circles around the conductor. Field strength
reduces with increase in radius from the centre; hence, subsequent circles are further
apart.
- Field is obtained using Flemming’s right hand grip rule.

pg. 4
FORCE ON A CURRENT – CARRYING CONDUCTOR IN MAGNETIC FIELD

- The combined effect of the field on a current carrying conductor in a magnetic field is
as shown below:

(as viewed from A)

- A force acts on a current-carrying conductor when it is placed in a magnetic field. The

magnitude of this force increases with increase in current and therefore field strength.
- The force is maximum when the angle between the conductor and the field is 900
and becomes zero when the conductor is parallel to the field.
- The force also increases with increase in the length of the conductor in the magnetic
fields.
- The fields tend to concentrate more on one side than the other as shown above.
- The weak field is due to the two fields opposing each other. Magnetic lines of force
act like elastic bands, concentration of the lines on the other side of the conductor
produces a catapult effect that pushes the conductor in the opposite direction.
- When the direction of current or magnetic field is reversed, the direction of the force
on the conductor also reverses.
- For a conductor carrying current in a magnetic field the direction of the force acting
on it can be predicted using Fleming’s left hand rule.

pg. 5
 Fleming’s left hand rule states that:
If the left hand is held with the thumb, the first finger and the second
finger mutually at right angles so that the first finger points in the
direction of field and the second finger in the direction of the
current, then the thumb points in the direction of motion as shown

Example 2
Look at the diagram in fig. A in which a wire connected to a cell is placed in a magnetic
field. In what direction will the wire experience a force?

Answer
The conventional current will flow from the positive end of the cell, so within the
magnetic field, as observed in fig. B, it will be moving away from us. With the magnetic
field from north to south (towards the right), Fleming’s left hand tells us that the wire
will experience a force pushing it downwards.

pg. 6
STRENGTH OF ELECTROMAGNETIC FORCES
- The force, F, on the wire which has a current, I, through it whilst it is in a magnetic
field, B, depends on:
(a) Size of current, I
(b) Strength of the magnetic field ,B
(c) Length of the conductor within the field, L
(d) Angle of interaction between conductor and field (900 being the maximum)
- The force is given by the equation:
𝑭 = 𝑩𝑰𝑳 𝐬𝐢𝐧 𝜽
- If the angle is 900, then:
𝑭 = 𝑩𝑰𝑳

𝜃 is the angle the current makes

with the magnetic fields.

Motor effect
- The forced movement of a current carrying conductor within a magnetic field is the
principle that causes motors to work (motor effect).
- From Fleming’s left hand rule, it is clear that a coil of wire experiences a turning force
if the wire is carrying a current and is put in a magnetic field. This is because the
current travels in opposite directions on opposite sides of the coil which causes forces
in opposite directions and rotates the coil. If it is free to move, then the coil (or
motor) will spin continuously. The apparatus below can be used to demonstrate
motor effect in the lab (remember to use low power d.c supply)

pg. 7
 The figure below shows a d.c motor:

- When the switch is closed current flows through the coil and generates a magnetic
field around it. When the magnetic field around the coil interacts with the magnetic
field of the permanent magnets, a force is exerted. According to FLHR opposite forces
of equal magnitude act on either side of the coil that makes it rotate.
- The split ring commutator reverses the direction of current in the coil after every half
turn which ensures that the coil rotates in the same direction. The carbon brushes
provide an electrical contact with split ring commutators.
- A motor can be made more powerful using the expression F = BIL:
Increasing the current through the motor

Increasing the number of turns of wire in the motor

Increasing the magnetic field within the motor

pg. 8
TASK
1. Figure 1 shows a vertical plane square coil of 50 turns, carrying a current of 3.0 A.
Thelength of each side of the coil is 4.0 cm. Figure 2 shows a view of this coil from
above within a horizontal magnetic field of flux density 0.20 T.

The force on side QS is

A 120 N
B 60 N
C 1.2 N
D 0.60 N
2. A 50 turn square coil, side 0.060 m, is placed in a magnetic field of flux density 0.40
T. The plane of the coil is at right angles to the direction of the magnetic field.

The flux linkage with the coil is

A 0.072 Wb
B 0.45 Wb
C 1.2 Wb
D 333 Wb
3. The diagram shows a horizontal wire which is at right angles to a magnetic field. The
magnetic field is produced by a horseshoe magnet which is on a balance adjusted to read
zero when the current in the wire is zero.

pg. 9
When the current is 4 A, the reading on the balance is 0.8 gram.
The length of wire in the magnetic field is 0.05 m.
Calculate the average magnetic flux density along the length of the wire.(3)

4. The simplified diagram shows a d.c. electric motor. The split ring commutator consists
of two copper semicircular sections attached to either end of a coil. Fixed carbon
brushes rub against, and make electrical connections to, the split ring commutator.

a) Explain why the coil turns and why it continues to rotate. Add to the diagram to
help your explanation. (4)
b) When the motor is first switched on the current I is large. As the coil turns faster,
the current decreases. Explain these observations. (4)

pg. 10
FORCE ON A CHARGED PARTICLE IN A MAGNETIC FIELD
- The motor effect happens because a charged particle moving at right angles to a
magnetic field experiences a force on it at right angles to its direction of motion and
also at right angles to the field.
- If the charged particle is constrained – like an electron in a current in a wire – then the
force will transfer to the wire itself.
- If the particle is flying freely, its direction will change and it will travel a circular path
while in the magnetic field as shown below.

- The direction of the force acting on a charged particle moving in a magnetic field can
be found using Fleming’s left hand rule.
- We must be careful with the current direction though: a negative charge moving in
one direction is a current flowing in the opposite direction.
- The strength of the force on a charged particle moving across a magnetic field is given
by the equation:

F = B x q x v x sin 𝜽

Where q is the charge on the particle, v is its velocity, and θ is the angle between the
velocity and the magnetic field lines.
- A simple situation that is often considered is that of an electron (charge, e) moving at
right angles to the field (sin 900 = 1). This reduces the formula to:

F = Bev

The following set up is used to investigate the magnetic force on a beam of charged
particles

pg. 11
 The grid allows you to observe the path travelled by
the electrons, and there is a standard formula for
calculating the magnetic field strength provided by a
pair of parallel electromagnetic coils, often referred
to as Helmholtz coils.

- As the force on the charged particle is always at right angles to the direction of its
velocity, it acts as a centripetal force, and the particle follows a circular path.
- As the charged particle’s velocity is constantly changing along a circular path, it is
being accelerated by the magnetic field.
- This means that given the right combination of conditions, a moving charged particle
could be held by a magnetic field, continuously orbiting a central point.
Scientists often need to identify unknown chemicals. This is particularly important, for
example, in the field of forensic science, where a crime scene technician will take a
sample of unknown material which they need to identify. A machine called a mass
spectrometer can separate chemicals according to their charge/mass ratio, which allows
unique identification of each substance within a sample.

A chemical to be identified enters the machine and is ionized. This charge will then allow
it to be accelerated in two different ways within the mass spectrometer.
An electric field increases its speed. Then it experiences a force when it travels through
the field of the electromagnet, which changes its direction.

pg. 12
The force on a charged particle moving at right angles to a magnetic field is given by:
𝐹 = 𝐵𝑞𝑣
Centripetal force is given by:
𝑚𝑣 2
𝐹= 𝑟

So for particles following the circuit curve through the electromagnet on a path to the
detector:
𝑚𝑣 2
𝐵𝑞𝑣 = 𝑟

Which rearranges to:

𝒒 𝒗
=
𝒎 𝑩𝒓

The charge/mass ratio will identify the particles involved, so with B and r (radius of the
curvature of the particle through the mass spectrometer) known from calibration of the
machine, all we need to know is how fast the particles were moving when they entered
the electromagnet.
The electric field acts on their charge and accelerates them to this speed, and the kinetic
energy gained comes from the potential difference, V, that they pass through according
to:
1
𝑚𝑣 2 = 𝑞𝑉
2

Which gives

pg. 13
 2𝑞𝑉
𝑣= √ 𝑚

Substituting this into our equation for the charge/mass ratio:

𝑞 √2𝑞𝑉/𝑚
=
𝑚 𝐵𝑟

Squaring gives:
𝑞2 2𝑞𝑉/𝑚
=
𝑚2 𝐵2 𝑟 2

𝑚 𝑞2 𝑚 2𝑞𝑉
𝑥 = 𝑥
𝑞 𝑚2 𝑞 𝑚𝐵2 𝑟 2

𝒒 𝟐𝑽
=
𝒎 𝑩𝟐 𝒓𝟐

Task
1. (a) A company selling sea salt for cooking wanted to find out if its ratio of chlorine
isotopes was different from the usual abundance ratio. In nature, the 35Cl isotope is
more common than the 37Cl one by a factor of 3:1. They analysed a sample of their
product using a mass spectrometer that would ionize the chlorine atoms into single
minus ions. What would be the difference between the radii of curvature caused for
the chlorine isotopes, if the mass of the spectrometer operated at an accelerating
potential of 3.0kV and had a magnetic field strength of 3.0T?

(b) For the investigation of salt above, calculate the difference in the radii of
curvature that would be found if the company investigated the two isotopes of
sodium 23𝑁𝑎 + and 22𝑁𝑎 + . Explain why such small difference can be easily detected by
a mass spectrometer.

2. (a) How much force would be felt by a 12cm wire carrying 0.8 A at right angles to
the Earth’s surface magnetic field of 5 x 10-5T?

(b) How much force would be felt by a proton travelling across the Earth’s magnetic
field at 500ms-1?

(c) How fast would a proton need to travel in order for the electromagnetic force on
it to make it orbit the Earth at the surface? (radius of Earth = 6.4 x 106 m). comment
on your answer.

pg. 14
ELECTROMAGNETIC INDUCTION (EMI)
- This is defined as the process of creating an induced voltage when a conductor cuts
through a magnetic field.

Figure 1:
When the conductor is moved
perpendicular to the field, the
galvanometer deflects. This shows that a
voltage is induced.

Figure 2:
When the magnet is moved into the coil or
out of the coil, the galvanometer deflects.
This shows that a voltage is induced.

A voltage is induced when:

a) The conductor moves perpendicular to the magnetic field.
b) The magnet is moved at right angles to the stationary conductor.
No voltage is induced when:
a) The conductor moves parallel to the magnetic field.
b) The magnet is moved with the wire stationary in the direction of the magnetic field.
c) Magnet and conductor moving at the same speed(no relative motion)

pg. 15
Explaining electromagnetic induction

B into the book

Conductor

A e e e e e e e e B

G
- If the conductor moves downwards with its free electrons, it is the same as
conventional current moving upwards.
- The charged particles in motion create their own magnetic field.
- The interaction between the two fields will produce a force whose direction is
predicted by use of Fleming’s Left Hand Rule.
- This force makes the electrons to move from B to A.
- Side B becomes positive and A becomes negative creating a net potential difference
that will produce a current in the external circuit.
- The direction of this current can be predicted using Fleming’s Right Hand Rule.

pg. 16
The magnitude of the induced e.m.f is increased by:
a) Increasing the number of turns in the coil
b) Increasing the strength of the magnet
c) Increasing angular velocity (speed of relative motion)
d) Increasing the angle of conductor in the field
These factors were summarized by Michael Faraday in what we call Faraday’s law of EMI
– which states that: the induced electromotive force is proportional to the rate of change
of flux linkage.
𝒊𝒏𝒅𝒖𝒄𝒆𝒅 𝒆𝒎𝒇 𝜶 𝒓𝒂𝒕𝒆 𝒐𝒇 𝒄𝒉𝒂𝒏𝒈𝒆 𝒐𝒇 𝒇𝒍𝒖𝒙 𝒍𝒊𝒏𝒌𝒂𝒈𝒆
𝒅∅
𝜺 = −
𝒅𝒕
(The minus sign will be explained using “Lenz’s law)
INDUCED EMF AND FLUX LINKAGE

Magnetic flux for a single conductor

∅ = BA
When B is the field strength of the magnet, the induced current passes through all the
coils in the same direction hence, the magnetic field increases with each additional coil.
Total magnetic flux linking all the coils is hence directly proportional to the number of
turns:

1 turn ∅ = BA (Wb)

Total flux for N coils:

∅ = NBA

pg. 17
Example
If the coil has 50 complete turns with a magnetic field of 20mT and the radius of coil is 5
cm. Calculate:
Answer

∅ = NBA
= 50 x 20 x 10-3 x π (0.05)2
= 7.85 x 10-3 Wb

Generator effect
The generator uses the same working principle of motor effect where the rotation of the
coil inside the magnetic field causes a change in magnetic flux linkage, which in turn
induces an emf across the coil.

In the rotating armature of the generator, the magnet provides a stationary magnetic
field. The coil, acting as the armature, rotates in the field, cutting the lines of force and
producing the desired output voltage. The output voltage is taken from the coil by the
slip rings and brushes.
One slip ring is attached to each end of the rotating coil. The brushes make sliding
electrical contact with the slip rings. The generator's output voltage can be transferred
from the slip rings through the brushes to an external circuit.

pg. 18
In a complete circuit, the e.m.f will cause a current to flow, and as the polarity
(direction) of the e.m.f is constantly switching, the current will keep changing direction.
This can be seen on the graph below, where the y-axis labelled ‘output’ could, with
appropriate units, refer either to the e.m.f across the bulb or the current through it.

The emf induced in the coil can be increased by:

Increasing the number of turns of the coil
Increasing the area of the coil
Increasing magnetic field strength
Increasing angular speed of the coil

TASK
1. A circular loop of thin wire is placed so that its plane is perpendicular to a magnetic
field as shown.

As the switch is closed, the loop of wire will

A become a circle of smaller radius.
B not change.
C rotate about its centre.
D rotate so that its plane is parallel to the field.

pg. 19
2. A strong magnetic field of flux density B can be used to trap a positive ion by making
it follow a circular orbit as shown.

Explain how the magnetic field maintains the ion in a circular orbit. You may add to
the diagram above if you wish.(2)

3. A coil of N turns and cross-sectional area A lies perpendicular to a magnetic field of

flux density B. The magnetic flux linkage is X. A second coil with twice the number of
turns but half the cross-sectional area lies perpendicular to a magnetic field of flux
density 2B. The magnetic flux linkage with the second coil is

4. The diagram represents a simple induction motor. An alternating current Is is supplied

to a stationary coil (stator). This coil is wrapped around an iron core.

A rotating coil (rotor) is shown end on in the diagram.

pg. 20
(a) The graph shows the variation of the alternating current Is with time.

*(i) Explain how current is induced in the rotor coil.(4)

(ii) Explain why the rotor turns.(2)

(iii) State two ways of making the rotor turn faster.(2)

(b) An induction motor is used to rotate the turntable in a record deck. Long-play
records require the turntable to rotate at 33 revolutions per minute.

(i) Calculate the angular velocity of the turntable.(3)

(ii) Calculate the acceleration of a speck of dust at the outside edge of a rotating
record.
radius of record = 12.5 cm(2)

5. The diagram shows an end view of a simple electrical generator. A rectangular coil of
wire is rotated in a uniform magnetic field of magnetic flux density 3.0 × 10–2 T. The
axis of rotation is at right angles to the field direction.

(a) The coil has 200 turns and an area of 2.0 ×10–4 m2.

pg. 21
Calculate the magnetic flux linkage for the coil when 𝜃 = 00. (2)

(b) The coil is rotated at a constant rate of 2 revolutions per second.

(i) Calculate the average e.m.f. induced in the time taken for the coil to rotate from 𝜃 =
00 to θ = 900 (3)
(ii) The graph shows how the induced e.m.f. varies over one cycle of rotation of the
coil.

Explain why the magnitude of the e.m.f. is smallest and greatest at the values of 𝜃
shown in the graph.(3)
(iii) State and explain how the graph would differ if the coil rotated at a slower rate.(2)
(c) Vehicles such as electric cars are driven by electric motors. These vehicles use
regenerative braking to reduce the speed of the vehicle. The motor is operated as a
generator during braking and the output from the generator is used to recharge the
batteries of the car.
(i) Explain how using the motor as a generator slows the car down.(2)
(ii) In practice, these vehicles also use friction braking as well as regenerative
braking. This is because regenerative braking on its own will not fully stop a car.
Suggest why.(2)

pg. 22
Lenz’s law
- Lenz’s law states that:
“The direction of an induced emf is such as to oppose the change creating it.”
- In other words, when you induce a current in a wire via a changing magnetic field,
the current flows through the wire in such a direction so that its magnetic field
opposes the change that produced the current.

- So, what happens when you induce a current by, say, moving a wire through a
magnetic field, is that you're converting mechanical energy (the energy of the wire's
motion) into electrical energy (the energy carried by the induced current).

- Lenz's Law ensures that the mechanical energy of the wire is reduced by the same
amount of energy gained by the current. It does this by exerting a force on the wire
opposing the wire's motion. This causes the wire to lose mechanical energy (its
motion is impeded); it must do work against the induced magnetic field to generate
current.

- Hence, Lenz’s law is a consequence of law of conservation of energy.

S N
S N

Magnet moving away

Magnet moving into the coil
The galvanometer deflects
The galvanometer deflects to
the left
the right

Lenz’s law and Faraday’s law combined

- Using Faradays law of electromagnetic induction, induced emf is proportional to the
rate of change of magnetic flux through a conductor
𝒅∅
𝜺 = −
𝒅𝒕
- The negative sign indicates that the induced emf is opposite in direction to the change
producing it (Lenz’s law)
- If the conductor has N turns:

𝐝∅
𝛆 = −𝐍 but ∅ = BA
𝐝𝐭

pg. 23
 𝐍𝐝𝐁𝐀
𝛆 = −
𝐝𝐭

- If a single conductor has length l, and it moves through a magnetic field of strength,
B, at a velocity, v, then it means:
𝐍𝐝𝐁𝐀
From 𝛆 = −
𝐝𝐭

𝑁 = 1, 𝐴 = 𝑙𝑣 𝑎𝑡 𝑡 = 1

Therefore 𝜺 = −𝑩𝒍𝒗

Examples
1. A 1.5 V cell is connected to a switch S, a neon lamp and a coil with many turns as
shown. Nothing is observed when the switch is closed but the neon lamp flashes as
soon as it is opened.
The neon lamp flashes when the potential difference across it is about 200 V.

Use Faraday’s law to explain why the lamp flashes once when the switch S is opened.(4)

Answer
Current in coil generates magnetic field in the coil
When switched off current drops/decreases in the coil
There is a change of flux [accept flux cut] which takes place rapidly/quickly/within a short
time
Large emf/200 V is induced since flux linkage is large due to many turns

pg. 24
2. *Faraday’s and Lenz’s laws are summarized in the list of formulae as
𝐝(𝐍∅)
𝛆 = −
𝐝𝐭
(a) State the meaning of the term 𝐍∅. (2)

Answer
(Magnetic) Flux
linkage

(b) Explain the significance of the minus sign.(3)

The minus sign is due to Lenz’s law / conservation of energy
The law states that induced current/emf (direction), opposes the change (that produced
it)

The copper tube example

- If you drop a magnet down a copper tube, it will drop slower than a non-magnetic
metal through it. This is the result of Lenz’s law.
- As the magnet falls through the tube, it will induce an e.m.f in copper tube, which
will cause a small current to flow around the tube. The circling current will then
generate an electromagnetic field, which will interact with the falling magnet. The
direction of this newly created magnetic field will determine whether it slows the
falling magnet or repels it faster down the tube.
- If the latter were the case, then the magnet would end up with more kinetic energy
than the gravitation potential it had at the start. This is impossible, so the law of
conservation of energy dictates the Lenz’s law.
- The e.m.f in the tube is such that it slows the magnet, as the movement of the magnet
is the change creating the e.m.f.

pg. 25
Lenz’s law graph
If a bar magnet is dropped through a coil as shown below, the graph below is abtained:

- The negative part of the peak is higher.

- Area under the graph both part of the graph will be same since Nφ is constant.
- As the magnet enters the coil, there is rate of change of magnetic flux linkage that
induces an e.m.f across the coil. As the magnet enters the coil, there is a force on it in
the upward direction to oppose the magnet’s motion according to Lenz’s law.
- As the magnet leaves the coil, the current direction reverses to oppose the magnets
motion again so suggested by the induced e.m.f being positive at first and then
negative.

pg. 26
- The negative maximum of the e.m.f is greater than the positive maximum as the
magnet has a greater speed while leaving than entering, since it is accelerating due to
gravity.
- The area under the graph while entering is equal to the area while leaving as the area
represent the total change in flux linkage which remains the same.

RESEARCH WORK:
Research on: eddy current and back e.m.f

TASK
A teacher demonstrates electromagnetic induction by dropping a bar magnet through a
flat coil of wire connected to a data logger.

The data from the data logger is used to produce a graph of induced e.m.f. across the
coil against time.

pg. 27
*(a) Explain the shape of the graph and the relative values on both axes.(6)

(b) The teacher then sets up another demonstration using a large U-shaped magnet and a
very small coil of wire which is again connected to a data logger.
The north pole is vertically above the south pole and the coil is moved along the line
AB which is midway between the poles. The magnetic field due to the U-shaped
magnet has been drawn. The plane of the coil is horizontal.

Sketch a graph to show how the e.m.f. induced across the coil varies as the coil
moves from A to B at a constant speed.(4)

pg. 28
MUTUAL INDUCTION

- The process by which an e.m.f is induced in one circuit by a change of current in a

neighboring circuit is called mutual induction.
- Flux produced by a current in a circuit A threads or links circuit B. When there is a
change of current in circuit A, there is a change in the flux linking coil B, and an emf is
induced in circuit B while the change is taking place.

A B

- Circuit A, is called primary circuit and B is called secondary circuit. The change in the
flux in the primary circuit is done by switching on and of the current.
- Mutual induction is more pronounced when the two coils are all wound on soft iron
ring. The ring enables all magnetic flux of the primary to form concentric loops within
it-thus reaching the secondary coil.

Secondary circuit

Magnetic flux of primary

Primary circuit forms circular loops

- Increasing the number of turns in the secondary coil also increases the induced e.m.f.
Experiments show that the e.m.f in the secondary coil is:
 Directly proportional to the e.m.f in the primary coil and
 Depends on the ratio of the number of turns in the secondary coil to the number
of turns in the primary coil

pg. 29
Example
The diagram represents two coils. Coil X has 1000 turns and a cross-sectional area of
10 cm2. It is carrying a current which produces a field of magnetic flux density 0.002 T.
Coil Y has 50 turns and a cross-sectional area of 4 cm2.

The flux linkage with coil Y is

Electromagnetic induction is applied in many areas. Some of these are:

Transformer, Moving-coil micro phone, A.C generator, Induction coil, D.C generator,
Bicycle dynamo

pg. 30
TRANSFORMERS
- Used to step up or step down an input a.c voltage.
- The working principle of a transformer relies on Faraday’s law.

- The a.c current in the primary coil produces a changing magnetic field.
- This causes a change in magnetic flux linkage through the secondary coil. According to
Faraday’s law a voltage is induced on the secondary coil.
- The introduction of the iron core ensures maximum flux linkage which in turn
enhances the efficiency of the transformer.
- The iron core of the transformer is insulated so that it is not heated up due to flow of
eddy currents.
- The output voltage, the input voltage and the number of turns in either coil is linked
by the equation:
Vp Ns
=
Vs Ns

- For an ideal transformer (100% efficient)

Power output = power input

Vs Is = Vp Ip

pg. 31
Example
Two coils, L and M, are placed next to each other as shown.

There is an alternating current in coil L. An alternating potential difference is produced

across coil M.
Which of the following changes will not increase the maximum potential difference
across M?
A Increasing the frequency of the alternating current.
B Increasing the magnitude of the current in coil L.
C Increasing the number of turns on coil M.
D Increasing the separation of L and M.
Answer
The only correct answer is D because moving the coils further apart decreases their maximum flux
linkage and therefore the maximum rate of change of flux linkage and maximum e.m.f.
A Is not correct because increasing the frequency increases the maximum rate of change of flux
linkage and therefore the maximum e.m.f.
B Is not correct because increasing the magnitude of the current increases the maximum magnetic
flux density and therefore increases the maximum rate of change of flux linkage and therefore the
maximum e.m.f.
C Is not correct because increasing the number of turns increases their maximum flux linkage and
therefore the maximum rate of change of flux linkage and maximum e.m.f.

pg. 32
TASK
The photograph shows a digital clamp meter or ‘amp-clamp’. This can be used to
measure the current in the live wire coming from the mains supply without breaking the
circuit.

The ‘jaws’ of the clamp are opened, placed around the wire carrying the current and
then closed. Inside the ‘jaws’ is an iron core with a coil of wire wrapped around it.
*(a) Explain how an e.m.f. would be produced in the coil of wire inside the amp-clamp
when the ‘jaws’ are placed around a wire carrying an alternating current.(4)

(b) State why the amp-clamp cannot be used with a steady direct current.(1)

(c) The amp-clamp cannot be used with a cable that is used to plug a domestic appliance
like a lamp into the mains supply.
Explain why not.(2)

(d) (i) Explain why the amp-clamp can be used to determine the magnitude of different
alternating currents with the same frequency.(2)

(ii) The amp-clamp may not be reliable when comparing alternating currents of
different frequencies.
Suggest why not.(2)

pg. 33
Energy Losses in a Transformer

1. Flux leakage
Not all the magnetic flux from the primary passes through the secondary coil. The geometric
design is optimized to ensure that the magnetic flux in each coil of the secondary is nearly the same
as that in each coil of the primary. E.g. the secondary coil being wound over primary coil.

2. Resistance of coil (Copper losses)

There will always be power dissipated in the form of heat through the resistance of current-carrying
conductors. Because transformers require such long lengths of wire, this loss can be a significant
factor. For a given material, the resistance of the coils can be reduced by making their cross section
large. The resistivity can also be made low by using high purity copper.

3. Hysteresis Loss
All ferromagnetic materials tend to retain some degree of magnetization after exposure to an
external magnetic field. This tendency to stay magnetized is called "hysteresis," and it takes a certain
investment in energy to overcome this opposition to change every time the magnetic field produced
by the primary winding changes polarity. This means that the energy required to magnetise the core
(while the current is increasing) is not entirely recovered during demagnetization. The difference in
energy is lost as heat in the core.

4. Eddy currents (Core Losses)

Because iron is a conductor of electricity as well as being an excellent "conductor" of magnetic flux,
there will be currents induced in the iron just as there are currents induced in the secondary windings
from the alternating magnetic field. These induced currents tend to circulate through the cross-section
of the core perpendicularly to the primary winding turns. Their circular motion gives them their unusual
name: like eddies in a stream of water that circulate rather than move in straight lines. Consequently,
these "eddy currents" must overcome significant electrical resistance as they circulate through the
core. These can be reduced by laminating the core

pg. 34