ES2C6 – Electromechanics 3 – Electromagnetism
Electromagnetism
Electromagnets are cheap and convenient, and closing the loop improves the control over them,
allowing for coarser, simpler devices to be used to get a precise effect.
Electrical Machines
Any electromagnetic machine can be considered to comprise of three functional elements:
1. Any electrical machine can create a magnetism on demand.
2. There needs to be something to channel the magnetic field.
3. Something to be usefully acted on by the field is needed in the machines.
Magnetic Structure
Magnets are dipoles, meaning they have a north seeking pole and south seeking pole. A magnet can
be halved and will always have a north and south pole. A magnetic field is caused by a moving
charge – whether that is an electron spinning or a large-scale current flow.
Magnetic Fields
Faraday described a magnetic field as “a region of influence, where a force can act on a particle”. A
magnet will have field lines, which are closed loops emitting from the north pole and returning to
the south pole on the outside of a magnet, on the inside the magnetic field lines move from the
south pole to the north. The lines imply equal field strength – so can never cross – and always act to
shorten themselves and follow the path of least resistance to get the magnetic energy back to the
south pole.
Electricity and Magnetism
In 1820, Oersted discovered that if a current was passed through a wire by a magnet it would have
an effect on the magnet.
A moving charge creates a magnetic field, with a large-scale charge movement – a flow of current –
in the same direction giving a dominant effect and the charge moving around the atom giving a
secondary effect. The field radiates outwards from a current carrying conductor, reducing in
strength as the distance increases.
Ampère discovered that the field strength, 𝐵, changed in proportion to the applied current, 𝐼, and in
inverse proportion to the distance from the conductor, 𝑅:
𝜇0 𝐼
𝐵= (1)
2𝜋𝑅
−2 −1
where 𝐵 is measured in 𝑇 or 𝑊𝑏𝑚 and 𝜇0 is the constant of permeability in 𝐻𝑚 . This means
that the current can be used to set the field value and that the field strength is a function of distance
from the conductor and the intervening material.
Magnetic Flux
Magnetic flux can be considered to be the magnetic equivalent to electrical current. It is measured
in 𝑊𝑏 and denoted by Φ. As the magnetic field is also given by:
Φ
𝐵=
𝐴
changing the area can also affect the concentration of the field.
7
, ES2C6 – Electromechanics 3 – Electromagnetism
Loops
If two electromagnetic fields of identical strength but opposite direction are placed next to each
other they will effectively cancel one another out and there will be no magnetic field acting. If they
are acting in the same direction and placed side-by-side their magnetism will combine to create a
stronger field.
They total flux is the flux linkage:
𝜆 = 𝑁Φ (2)
Channelling
Some materials are easier to magnetise than others, depending on their permeability – how well a
material builds a field under the influence of a magnetising source. A coil of 𝑁 turns carrying a
current 𝐼 and with a length 𝐿 developed a magnetic field intensity 𝐻, measured in 𝐴𝑡𝑚−1 , or amp-
turns per metre:
𝑁𝐼
𝐻= (3)
𝑙
The higher the permeability, the more useful the magnetic field will be:
𝐵 = 𝜇𝐻 (4)
The material permeability is usually given in terms of the permeability of free space and the relative
permeability of the material:
𝜇𝑚 = 𝜇𝑟 𝜇0 (5)
−1 7 −1
in 𝐻𝑚 . Where 𝜇0 = 4𝜋 × 10 𝐻𝑚 .
Cores
Ferromagnetic materials are especially good at developing a magnetic field as they have high 𝜇
values. Each magnet is made up of dipoles which can organise into domains. When there is no
magnetic field the domains will be oriented randomly. However, when a magnetic field is
introduced, most domains align with the field, creating a net alignment in the direction of the field
which may cause some effects to remain even after the field is removed.
Permeable cores channel flux and can be used to create an iron circuit. A strong field is used to
create a high flux density. In comparison to the surrounding air, the permeability of the core is much
higher, so the flux stays within the core.
Forces
If a current is passed through a wire within a magnetic field a force will act on it. Half of the flux
rotating around the current will be acting with the original magnetic forces and the other half will be
acting against them. This causes the wire to be pushed away, towards where the fluxes are opposing
one another.
Galvanometers
A galvanometer consists of a fine wire with many turns. The wire is within a magnetic field and
current causes deflection against a retaining coil spring. The galvanometer comes to rest when the
spring force balances the magnetic force. Using cylindrically shaped poles makes the field act radially
and the plane of the wire loops move in line with the field lines, linearizing the output so:
𝑁𝐴𝐵
𝜃= (6)
𝜅𝐼
8
Electromagnetism
Electromagnets are cheap and convenient, and closing the loop improves the control over them,
allowing for coarser, simpler devices to be used to get a precise effect.
Electrical Machines
Any electromagnetic machine can be considered to comprise of three functional elements:
1. Any electrical machine can create a magnetism on demand.
2. There needs to be something to channel the magnetic field.
3. Something to be usefully acted on by the field is needed in the machines.
Magnetic Structure
Magnets are dipoles, meaning they have a north seeking pole and south seeking pole. A magnet can
be halved and will always have a north and south pole. A magnetic field is caused by a moving
charge – whether that is an electron spinning or a large-scale current flow.
Magnetic Fields
Faraday described a magnetic field as “a region of influence, where a force can act on a particle”. A
magnet will have field lines, which are closed loops emitting from the north pole and returning to
the south pole on the outside of a magnet, on the inside the magnetic field lines move from the
south pole to the north. The lines imply equal field strength – so can never cross – and always act to
shorten themselves and follow the path of least resistance to get the magnetic energy back to the
south pole.
Electricity and Magnetism
In 1820, Oersted discovered that if a current was passed through a wire by a magnet it would have
an effect on the magnet.
A moving charge creates a magnetic field, with a large-scale charge movement – a flow of current –
in the same direction giving a dominant effect and the charge moving around the atom giving a
secondary effect. The field radiates outwards from a current carrying conductor, reducing in
strength as the distance increases.
Ampère discovered that the field strength, 𝐵, changed in proportion to the applied current, 𝐼, and in
inverse proportion to the distance from the conductor, 𝑅:
𝜇0 𝐼
𝐵= (1)
2𝜋𝑅
−2 −1
where 𝐵 is measured in 𝑇 or 𝑊𝑏𝑚 and 𝜇0 is the constant of permeability in 𝐻𝑚 . This means
that the current can be used to set the field value and that the field strength is a function of distance
from the conductor and the intervening material.
Magnetic Flux
Magnetic flux can be considered to be the magnetic equivalent to electrical current. It is measured
in 𝑊𝑏 and denoted by Φ. As the magnetic field is also given by:
Φ
𝐵=
𝐴
changing the area can also affect the concentration of the field.
7
, ES2C6 – Electromechanics 3 – Electromagnetism
Loops
If two electromagnetic fields of identical strength but opposite direction are placed next to each
other they will effectively cancel one another out and there will be no magnetic field acting. If they
are acting in the same direction and placed side-by-side their magnetism will combine to create a
stronger field.
They total flux is the flux linkage:
𝜆 = 𝑁Φ (2)
Channelling
Some materials are easier to magnetise than others, depending on their permeability – how well a
material builds a field under the influence of a magnetising source. A coil of 𝑁 turns carrying a
current 𝐼 and with a length 𝐿 developed a magnetic field intensity 𝐻, measured in 𝐴𝑡𝑚−1 , or amp-
turns per metre:
𝑁𝐼
𝐻= (3)
𝑙
The higher the permeability, the more useful the magnetic field will be:
𝐵 = 𝜇𝐻 (4)
The material permeability is usually given in terms of the permeability of free space and the relative
permeability of the material:
𝜇𝑚 = 𝜇𝑟 𝜇0 (5)
−1 7 −1
in 𝐻𝑚 . Where 𝜇0 = 4𝜋 × 10 𝐻𝑚 .
Cores
Ferromagnetic materials are especially good at developing a magnetic field as they have high 𝜇
values. Each magnet is made up of dipoles which can organise into domains. When there is no
magnetic field the domains will be oriented randomly. However, when a magnetic field is
introduced, most domains align with the field, creating a net alignment in the direction of the field
which may cause some effects to remain even after the field is removed.
Permeable cores channel flux and can be used to create an iron circuit. A strong field is used to
create a high flux density. In comparison to the surrounding air, the permeability of the core is much
higher, so the flux stays within the core.
Forces
If a current is passed through a wire within a magnetic field a force will act on it. Half of the flux
rotating around the current will be acting with the original magnetic forces and the other half will be
acting against them. This causes the wire to be pushed away, towards where the fluxes are opposing
one another.
Galvanometers
A galvanometer consists of a fine wire with many turns. The wire is within a magnetic field and
current causes deflection against a retaining coil spring. The galvanometer comes to rest when the
spring force balances the magnetic force. Using cylindrically shaped poles makes the field act radially
and the plane of the wire loops move in line with the field lines, linearizing the output so:
𝑁𝐴𝐵
𝜃= (6)
𝜅𝐼
8
