PHYS1000
Electricity & magnetism
1
Electromagnetism
Moving an electric charge
A charge in an electric field will experience a force due to the field; if the charge is not held in place
by some other force, it will move.
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Dielectrics (insulators) and conductors
In a solid, the atoms are held in a fixed position by forces from the surrounding atoms.
• DIELECTRIC (INSULATOR)
The atoms holds all of its electrons in place – no charges will move far from their usual positions. A small amount of motion is possible:
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As a result, the material becomes electrically polarised. The overall effect is to make one surface
positively charged, and the other negatively charged. The electric field from these polarisation
charges reduces the electric field in the material.
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Electricity & magnetism
PHYS1000
2
The electric field in a dielectric is:
Edielectric =
1
1
Eapplied = Eapplied
κ
The constant κ (or ) is called the dielectric constant or relative permittivity or the material.
Just replace 0 in electrical formulae by κ 0 (or k by k/κ )
• CONDUCTOR
Some of the electrons are equally attracted by all of the nearby atoms – these electrons (conduction electrons) can freely move.
– Charges in a conductor move until the electric field produced by the moved charges cancels the applied electric field.
– If the conductor and field are made so that the total charge everywhere is zero (eg by using
a conducting loop), an electric current can be produced and maintained
Electric current
A steady electric current can be produced in a conductor that allows the electrons to return to their
starting positions.
We measure the strength of the current by how much charge moves through a section of the conductor is a given time. The SI unit of electric current is the ampere (A). 1 A = 1 C/s.
Note that, since the electric charge of an electron is negative, electrons actually move in the direction
opposite to the current.
Resistance & Ohm’s law
As the charges move through a material, they lose energy through collisions with the molecules
making up the material. We describe this by the resistance of the material. The SI unit of resistance is
the ohm (Ω).
An applied electric field can keep them moving at a constant speed. Since the potential difference
along an electric field is ∆V = E∆x, we can find the current using Ohm’s law
V = IR
How much energy do the moving charges lose? This energy is replaced by the work done by the
electric field. Since w = QV, the power (ie work per second) lost to the material due to resistance is:
P = VI
Magnetic fields & forces
We find that moving charges exert a force on each other. This force is a magnetic force, and has a
magnetic field associated with it.
PHYS1000
Electricity & magnetism
3
• Moving charges produce magnetic fields
EXTRA The magnetic field produced by a moving charge is
B=
µ0 q
(v × r)
4π r2
The constant µ0 = 4π × 10−7 M·s2 /C2 = 1.26 × 10−6 M·s2 /C2 is called the permeability of free
space or the permeability constant.
ADVANCED The magnetic field produced by a moving charge is at right angles to the direction of motion. You can find the direction of the field by using the right-hand rule
position
motion
B field
(out from palm)
Since an electric current is made up of moving charges, electric currents produce magnetic
fields.
ADVANCED The magnitude of the magnetic field produced by a current in a long, straight
wire is
B=
µ0 I
2π r
• Magnetic fields exert forces on moving charges
ADVANCED A charge moving in a magnetic field experiences a force at right angles to its
motion:
F = q(v × B)
The direction can be found using a right-hand rule:
B field
motion
force
(out from palm)
PHYS1000
Electricity & magnetism
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Note that since the force and motion are at right angles, charged particles moving in magnetic
fields tend to move in circles.
Since an electric current is made up of moving charges, a magnetic field exerts a force on a wire
carrying an electric current.
ADVANCED The magnitude of the force exerted on a straight wire of length L is
F = BIL
We choose our SI units for electromagnetism so that the force between two long straight wires,
each carrying a current of 1 A is 1 N/m.
We use the symbol B or B for magnetic field. The SI unit is the tesla (T).
EXTRA Magnetic charge?
Note that the formulae for magnetic fields and forces all use electric charge. Is there such a thing as
magnetic charge? We note that magnetic fields produced by moving charges look as if they could
have been produced by two magnetic charges very close together – the field is a dipole field. Do
these charges actually exist? Physicists have looked for them, but haven’t found them, so we have to
assume that they don’t.
The Earth’s magnetic field
A dipole in an applied field tends to align along the field. Magnetic dipoles – for example, a bar
magnet – align in a particular direction relative to the earth. Why? The earth has a magnetic field (of
about 5 × 10−5 T).
The end of a magnet that points towards the north pole is called the north pole of the magnet, and
the other end is the south pole. Note that the north magnetic pole of the earth is actually a south pole
in magnetic terms.
Drawing magnetic field diagrams
Drawing magnetic field diagrams is very similar to drawing electric field diagrams.
• Since there are no magnetic charges, magnetic field lines must be continuous – they can’t start
or stop anywhere.
• Magnetic field lines produced by a current in a wire form circles around the wire.
• For a permanent magnet:
– Outside the magnet, the field lines go from the N pole towards the S pole.
– Inside the magnet, the field lines go from the S pole towards the N pole, with each field
line forming a complete loop.
PHYS1000
Electricity & magnetism
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Electromagnets
A loop of current produces a magnetic field:
A series of loops can be used to produce a stronger magnetic field:
Magnetic materials & permanent magnets
Consider an electron moving around an atom. The moving charge produces a magnetic field similar
to that of a wire loop.
If the atoms in a material are oriented randomly, the magnetic fields of the individual atoms will
cancel out.
The atoms can be temporarily aligned by an external magnetic field. This affects magnetic fields in a
similar way that dielectrics affect electric fields.
The atoms can also be permanently aligned – producing a permanent magnet.
ADVANCED Electric motors and generators
A wire carrying a current in a magnetic field experiences a force. This can be used to convert electrical
energy to mechanical work – an electric motor.
Consider a wire being moved through an electric field. The magnetic force moves charge along the
wire – this can be used to produce an electric current.