Unit 4-Physics On The Move
Topic 2-Electric and Magnetic Fields
Explain what is meant by an electric field and recognise and use the
expression for electric field strength E=
𝑭
𝑸
Charges and fields
Electric charge is one of the fundamental properties of nature. Two objects of the same charge will
push each other apart (repel) while objects of opposite charge pull each other together (attract).
Surrounding every charged object is an electric field-a region of space in which another charged
object will experience a force. The electric field is characterised by strength and direction. The
strength of the field at a point in space determines the size of the force that a charge will experience
if it is placed at that point. Electric field strength is a vector quantity. The direction of the field at a
point is defined to be the direction of the force acting on a small positive charge placed at that point.
When a field-line diagram is drawn to illustrate the nature of an electrical field, the arrows on the
field lines are always drawn to show the direction of the force on a positive charge.
𝐹
The electric field strength, E, at a point is the force, F, acting per unit charge, q, at that point : E=𝑄
Draw and interpret diagrams using lines of force to describe radial
and uniform electric fields qualitatively
The field of a point charge
The simplest electric field belongs to a single point charge (that is, a charge that is very small
compared with any distance that we may be measuring), like an electron


The strength of the field is proportional to the size of the charge
It varies with distance from the charge
As the charge only occupies a point in space, the field must look the same along any line that is
drawn radially from that point. The field lines spread out as they get further from the charge, which
indicates that the field is getting weaker.
The field of one more than one charge
The total force exerted on a charge by a collection of other charges can be calculated by adding up
each of the ‘one-on-one’ forces. This is because electric fields obey the principle of superposition.
The field at any point due to a collection of charges is the sum of the separate fields due to each
charge. In calculating the size of the field, or the force, one must remember that they are vector
quantities.
𝒌𝑸𝟏 𝑸𝟐
Use the expression F=
𝒌𝑸
expression E=
𝒓²
𝒓²
where k=
𝟏
𝟒𝝅𝜺₀
and derive and use the
for the electric field due to a point charge
𝑘𝑄 𝑄
The electrostatic force between two charges spherical objects obeys an inverse square law: F= 𝑟²1 2,
where Q₁ and Q₂ are the two charges, r is the separation of the centres of the two charged objects,
and k is a constant dependent upon the medium between the two charges. An equal magnitude
force acts on each charged object-the forces are repulsive for two like charges and attractive for two
opposite charged. The forces form Newton’s third law pair.
We can calculate the field strength at a position in a radial field by using Coulomb’s law. If the charge
producing the field is Q and a small charge in the field is q:
𝐹
𝑘𝑄𝑞
𝑘𝑄
E=𝑞 , and F= 𝑟² , so E= 𝑟²
The potential of a point charge
When an electric charges moves through a conductor, electric potential energy is converted into
thermal energy, and there is a p.d. across the conductor. One would expect a similar energy
conversion whenever one charge moves through the electric field of another. In many cases the
situation is far simpler than in an electric circuit, which has complicated patterns of charge on cell
plates or on the ends of components. An especially simple case is moving one point charge towards
or away from another that is fixed in place. In an electric circuit, the p.d. between two points in the
circuit is defined as the energy converted when a charge Q moves between two points in a circuit
per amount of charge Q. In a circuit, the difference in potential between two points is fixed by the
cells and components. When we are working with fields due to many large charges, the value of the
potential at a single point is often useful. A point infinitely far from the positive charge is defined as
having zero potential, and from this the value of the potential anywhere else in the field can be
defined. The sign of the potential is determined by the sign of the charge. As potential is a scalar
quantity, the sign is not telling us about direction. The significance of the sign is simply to indicate if
the potential is higher or lower than the zero at infinity.
Investigate and recall that applying a potential difference to two
parallel plates produces a uniform electric field in the central region
𝑽
between them, and recognise and use the expression E=
𝒅
Not all fields are radial. An example of a uniform electric field is found in the space between two
parallel plates, when there is a potential difference applied between the plates. There is a uniform
field between the plates, where the field lines are parallel and equally spaced. The strength of the
𝑉
uniform field between the plates is given by E=𝑑, where V is the potential difference between the
plates and d is their separation.
Investigate and use the expression C=
𝑸
𝑽
Capacitance
Any arrangement of two conductors isolated from one another by an insulator will form a capacitor.
In the lab this may be two sheets of metal with small pieces of plastic between. In this case air forms
the insulator. A commercial capacitor can be made by using sheets of wax paper to separate two
sheets of thin metal foil. Very large areas of foil can be rolled up and contained in small cylinders.
The two conductors forming the capacitor are always called the capacitor plates. Capacitors store
energy by keeping electrical charges on their plates (separating charge). They can also be viewed as
devices for storing charge. When a capacitor is charged up, one of the plates will have a positive
charge and the other an equal negative charge. A voltmeter connected between the plates will
record a p.d. The ratio between the charge and the p.d. is a constant for the particular capacitor, and
is called the capacitance. The capacitance is determined by the size of the plates, the nature of the
insulator and the way in which the plates are arranged. The unit used to measure capacitance is the
farad.
Recognise and use the expression W=½QV for the energy stored by a
capacitor, derive the expression from the area under a graph of
potential difference against charge stored, and derive and use related
expressions
Energy Stored In A Capacitor
When a cell is used to charge a capacitor, a certain amount of chemical energy is converted into
electrical energy. Some of this appears as thermal energy in the resistance of the charging circuit,
but this only accounts for half of the energy converted by the cell. The rest is stored in the capacitor.
This is shown by the ability of a capacitor to provide energy to drive a current as it is discharging. The
stored energy inside the capacitor is a form of potential energy


Any situation in which opposite charges are held apart from each other against the action of
their electrostatic attraction will store electrical potential energy
This is similar to the storage of gravitational potential energy when two masses are held
apart against their gravitational attraction
Investigate and recall that the growth and decay curves for resistancecapacitor circuits are exponential, and known the significance of the
time constant RC
Charging a capacitor
Charge starts to flow in the wires the instant that the cell is connected. As there is insulation
between the plates of the capacitor, electrons are forced to accumulate on the plate connected to
the negative side of the cell. Electrons move away from the other plate, partly because of the
repulsion from the negative charge nearby and partly because of the attraction of the positive side
of the cell. The initial current in the circuit is determined by the resistance r (which may just be the
resistance of the wires). Surprisingly, the uncharged capacitor does not resist the current arriving at
one plate or leaving the other. On a graph of capacitor charge against time, the initial current is the
gradient of the graph at the origin. As charge build up on the plates, it repels more charge than is
arriving and the current drops as the charge on the plates increases. Charging will stop when the p.d.
between the capacitor plates is equal to the e.m.f. of the cell.
Time constant
In principle, a capacitor can never charge up fully, because the rate of charging decreases as the
charge increases. In practice, after a finite time the charging current becomes too small to measure,
and the capacitor is effectively fully charged. The time taken to charge a capacitor in a given circuit is
determined by the time constant of the circuit. The bigger the capacitance, the longer it takes to
charge the capacitor. The larger the resistance, the smaller the current, which also increases the
charging time. The half time is the time taken to halve the charging current. After every time interval
t½, the amount of extra charge still needed to fully charge the capacitor halves.
Discharging a capacitor
A charged capacitor that is isolated from a circuit should hold its charge indefinitely. However,
leakage between the plates (due to the imperfect nature of the insulators) will eventually
completely discharge the capacitor. A capacitor can be deliberately discharged by connecting its
plates together via a resistor. On a graph of charge against time, the discharge current is given by the
gradient at any point. So the gradient of the curve is proportional to its value at any point. There is
only one type of curve in mathematics that has this property-the exponential curve. The time
constant determines the time taken to halve the amount of charge on the plates.
Energy is stored in the capacitor because work is done as charge moves through the net potential
difference in the circuit. This becomes electrostatic potential energy
−𝒕
Recognise and use the expression Q=Q₀𝒆𝑹𝑪 and derive and use related
expressions for exponential discharge in RC circuits
The discharging process is an example of exponential decay, or a constant ratio change. The time
taken for the charge on the capacitor to fall to a given fraction of the starting value is always the
same for a given circuit. This depends upon the capacitance, C, and resistance, R in the circuit.
Explore and use the terms magnetic flux density B, flux Φ and flux
linkage NΦ
Magnetic flux


The flux linked to a coil (Nφ) with multiple turns is the flux through one turn multiplied by
the number of turns
The flux cut by a moving wire is the magnetic field strength multiplied by the area swept out
by the wire
Lines representing the magnetic field in a given region are called ‘lines of magnetic flux’. The number
of lines passing through a unit area perpendicular to the field represents the flux density, B, and is a
measure of the magnetic field strength.
The e.m.f. induced in a circuit can be calculated from Faraday’s law of induction: e.m.f.= - rate of
change of flux. The minus sign indicates the direction in which the e.m.f. is induced.
Investigate, recognise and use the expression F=BIlsinθ and apply
Fleming’s left hand rule to currents
Fleming’s left-hand rule
The magnetic strength, B, the velocity of the charge, v, and the magnetic force F are all vector
quantities. In order to find the direction in which the force acts, given the direction of the field and
the velocity, Fleming devised a simple rule that uses two fingers and a thumb on the left-hand.
Fleming’s left-hand rule works for the other direction in which a positively charged particle is
moving; in other words, it is defined for conventional current. In the case when a particle is an
electronic, the second finger must point in the opposite direction to that in which the electron is
moving. Also note that the direction of the magnetic force is always perpendicular to the plane in
which the magnetic field and the charge’s velocity lie.
The force on a current-carrying wire
The magnetic force acting on an individual charged particle is too small to easily measure in the lab.
The effect of the force can be seen in the deflection of an electron beam, but for measurement
purposes the force on a current-carrying wire is more convenient. If the wire is crossed by a
magnetic field of strength B, each electron drifting along the wire will experience a magnetic force
equal to Bev. The total force acting on the wire is the sum of forces acting on each electron drifting
through it. This enables us to define one tesla as being the magnetic field strength required to exert
a force of 1 N on a wire of length 1 m carrying a current of 1 A. The magnetic force is acting on the
electrons within the wire. However, the electrons form part of the structure of the metal, and so the
force is passed on to the wire as a whole. This indirect force on current-carrying conductors is very
important technologically. Without this force, devices such as electric motors, loudspeakers, and
electric bells would not exist.
Magnetic field of a current-carrying wire
The shape of the magnetic field produced by a long straight wire is revealed by placing a ring of small
compasses on a card with the current-carrying wire passing through a hole in the centre. The
compasses turn to point in a closed circle round the wire, showing that the magnetic field lines form
circular loops centre on the wire. If the card is moved along the length of the wire, the compasses
stay pointing in circular loops. This shows that the compasses are drawing out a slice through a
magnetic field pattern that is actually cylindrical and centred on the wire. As magnetic fields are
vector quantities, a convention is required to specify their direction at any point in space.



The direction (or sense) of a magnetic field is specified by the way in which a small
geographical compass would point if placed in the magnetic field at that point
This is also the direction in which the magnetic force would act on a ‘free north pole’ if
monopoles existed
In the case of the field round the long wire, the sense is determined by the direction of the
current in the wire
Force between two current-carrying wires
If the currents in two parallel wires are in the same direction, the force is attractive. If the currents
are in opposite directions, the force is repulsive. This can cause problems if wires carrying large
currents need to be run next to one another, for example in overhead power lines.
Solenoid field
A solenoid is a tightly wound coil of wire


The coils should touch each other for the most uniform magnetic field
The wire must be insulated to prevent the current shorting between the wires
If one could wind an infinitely long solenoid from wire with a diameter that is much smaller then the
diameter of the solenoid itself, the field inside would be uniform. There would be no field outside
the solenoid. In practise, no solenoid can be finitely long, but the field outside is always very much
weaker than the internal field. The direction of the field can be found by matching the direction of
the current round the coil to arrows placed on the letters N and S. Magnetic field lines pass from N
to S outside the solenoid and form S to N inside the solenoid. The use of the letters N and S refers to
the fact that if the solenoid was hung from a thread and allowed to rotate freely, the N end would
point in a geographically northern direction.
Magnetic poles
It is often very difficult to work out the direction in which circulating currents would exert magnetic
forces on each other. The task can be simplified by the idea of magnetic poles. The north-seeking
pole of the solenoid is the end from which the magnetic field emerges. The other end is the south
seeking pole. A simple experiment shows that like poles repel, and unlike poles attract each other.
When like poles come together, the currents in the solenoids are circulating in a different direction,
and so will be repelling each other. Permanent bar magnets also have poles. Bringing two bar
magnets together will produce forces between the currents within them that can lead to attraction
or repulsion, depending on how they are aligned. It is not always possible to identify suitable poles in
a magnetic field. The field of a long, straight wire, for example, does not have poles. In such cases
the forces must be found using Fleming’s left-hand rule and the corkscrew rule. Poles are not the
magnetic equivalent of charges. There is no experimental evidence to suggest that magnetic charges
(monopoles) exist.
The turning force on a motor coil
An electric motor is basically a coil of wire carrying a current in a magnetic field. The forces acting on
the coil will, if properly arranged, tend to make the coil rotate. However, as the coil rotates the size
of the torque changes, so the rotation is not smooth. The size of the torque on the coil can be
increased by





Increasing the area of the coil
Increasing the current in the coil
Using more turns of wire in the coil
Using a stronger magnetic field
Making the magnetic field radial rather than uniform
The electric motor
Means of improving an electric motor:




Using curved end pieces to the permanent magnet, helping make the field radial
Using a cylindrical soft iron armature (rotating part) to increase field strength, and help
make it radial
Using more than one coil on the same axis, so one is nearly always parallel to the magnetic
field
Using a split-ring commutator. This swaps current direction every half turn, and stops the
wires becoming tangled
In most electric motors, the magnetic field is generated by wrapping a solenoid round a piece of iron
with curved end pieces. This is known as the field winding, to distinguish it from the armature
winding (the rotating coil) the two windings can be connected in series or in parallel. With a serieswound motor the same current flows in both coils


When the motor is stationary, a large current flows, because there is little resistance in the
coils, and there is a large torque on the armature to get it started
When the motor is rotating, electromagnetic induction produces an e.m.f. that opposes the
current which is consequently reduced in both coils
Motors using a.c. are also series-wound. With a.c. field winding, the magnetic field is continually
reversing. However, the torque in the armature does not reverse, as the current in that coil is
reversed as well. Motors using a.c. are useful in situations where it is inconvenient to use d.c., such
as in a mains-powered electric drill. In a shunt-wound motor, the field coil is connected in parallel to
the armature coil. The current in the coils is different, so there is no strong initial push, but the
rotation rate is more constant under varying load conditions.
Investigate and use the expression F=Bqvsinθ and apply Fleming’s left
hand rule to charges
Magnetic force on a point charge
A magnetic field is a region of space in which a moving electrical charge experiences a magnetic
force. Magnetic field strength needs to be defined in a different way to electric field strength
because magnetic forces are only exerted on moving charges. The size of the force acting is
proportional to the size of the charge and to the speed at which it is moving. If the path of the
charge is not at 90° to the magnetic field lines, then the angle between the path and the field lines
must also be taken into account.
Magnetically induced electric currents
The magnetic force on a moving charge can be used as a means of generating an electrical current.
Any piece of conducting material contains charges, and simply moving the material through a
magnetic field will result in forces being exerted on those charges. We normally think of magnetic
forces as acting on currents, but really they act on any moving charge-even the charges within a wire
that is moving. If a wire is moved at right angles to a magnetic field, then the magnetic force will
drive the electrons along the wire. Effectively, there is an electric current along the length of the
wire. The electrons collide with atoms as they drift along, so their kinetic energy is converted into
thermal energy. The electrons are as much a part of the wire as the atoms within it, so the wire is
also losing kinetic energy. This effect is known as current braking and can be used in practical
situations. If there is some way of removing charge at one end of the wire and replacing it at the
other, a continuous electrical current can be maintained in the wire.
Investigate and explain qualitatively the factors affecting the emf
induced in a coil when there is relative motion between the coil and a
permanent magnet and when there is a change of current in a primary
coil linked to it
Electromotive force (e.m.f.) across a moving wire
In the fairly simple situation of a straight wire moving through a magnetic field, the e.m.f. across the
wire can be calculated. A constant current can be maintained by having it roll along a wire loop. The
magnetic force acting on the electrons has a component perpendicular to the wire, which is the
force (BIl) that acts on any current-carrying wire. This force acts in the opposite direction to the
motion of the wire, and so an external force, F, is required to keep a constant speed.
The transformer
A transformer is a device for changing an alternating voltage from one value into another, and it
plays a significant part in the distribution and use of electric power. Transformers step up the
voltage produced by the generators to a very high value so that it can be transmitted efficiently to
the user. Transformers are constructed by wrapping two coils round a common piece of soft iron. In
order to ensure the efficient magnetic linkage between the coils, the core of the transformer is
usually a closed loop (a magnetic circuit). This helps the core to become uniformly magnetised. If the
primary coil is connected to an a.c. supply, an alternating magnetic field will be set up in the coil.
This will cause an alternating flux linkage in the secondary coil producing an e.m.f. by mutual
induction. A transformer’s core is often made of laminated iron-layers of iron sandwiched by an
insulator. This prevents the build up of eddy currents in the core whose magnetic fields disturb the
flux linkage, and whose heating effects reduce the efficiency of the conversion. The greater the a.c.
frequency, the thinner the laminations have to be. At very high frequencies it may be necessary to
use fine wires bundled together or iron dust packed into the core. Very high-frequency transformers
use cores made from non-conducting but magnetic materials, such as ferrites. These materials are
similar to ceramics, and so can be quite brittle, and are far less easily magnetised than soft iron.
Investigate, recognise and use the expression ε=−
𝒅(𝑵𝜱)
𝒅𝒕
and explain
how it is a consequence of Faraday’s and Lenz’s laws
Lenz’s law
The induced current is always in a direction that will help to counteract the change in flux that is
producing it.

If it were induced in the same direction, the field of the induced current would be in the
opposite direction to the external field. The two fields ten to cancel inside the loop, which
would reduce the flux linked, further inducing a greater current. This greater current would
have a greater magnetic field, which improves the cancellation, and the problem gets worse.
This situation would violate conservation of energy, as the current would increase almost
without limit
The amount of magnetic flux interacting with a coil of wire is known as the magnetic flux linkage.
Flux linkage = BAN. As F = Bqv, the faster the relative motion between a magnetic field and a
conductor, the greater the induced emf. This is Faraday’s law.
‘The magnitude of an induced emf is proportional to the rate of change of flux linkage’