# OCR AS/A Level Physics A

# Electric and magnetic fields

Navigate to resources by choosing units within one of the unit groups shown below.

## Introduction

### Overview

Delivery guides are designed to represent a body of knowledge about teaching a particular topic and contain:

- Curriculum Content: A clear outline of the content covered by the delivery guide
- Thinking Conceptually: Expert guidance on the key concepts involved, common difficulties students may have, approaches to teaching that can help students understand these concepts and how this topic links conceptually to other areas of the subject
- Thinking Contextually: A range of suggested teaching activities using a variety of themes so that different activities can be selected which best suit particular classes, learning styles or teaching approaches.

## Curriculum Content

### Overview

**Content (from A Level)**

**6.2 Electric fields**

This section provides knowledge and understanding of Coulomb’s law, uniform electric fields, electric potential and energy.

**6.2.1 Point and spherical charges**

(a) electric fields are due to charges

(b) modelling a uniformly charged sphere as a point charge at its centre

(c) electric field lines to map electric fields

(d) electric field strength; \(\displaystyle E=\frac{F}{Q}\).

**6.2.2 Coulomb’s law**

(a) Coulomb’s law; \(\displaystyle F=\frac{Qq}{4\pi\varepsilon _0r^2}\)

for the force between two point charges

(b) electric field strength \(\displaystyle E=\frac{Q}{4\pi\varepsilon _0r^2}\)

for a point charge

(c) similarities and differences between the gravitational field of a point mass and the electric field of a point charge.

(d) the concept of electric fields as being one of a number of forms of field giving rise to a force.

**6.2.3 Uniform electric field**

(a) uniform electric field strength; \(\displaystyle E = \frac {V}{d}\)

(b) parallel plate capacitor; permittivity;

\(\displaystyle C = \frac {\varepsilon_0A}{d}\); \(\displaystyle C = \frac {\varepsilon A}{d}\); \(\displaystyle \varepsilon = \varepsilon_r \varepsilon_0\)

(c) motion of charged particles in a uniform electric field.

**6.2.4 Electric potential and energy**

(a) electric potential at a point as the work done in bringing unit charge from infinity to the point; electric potential is zero at infinity

(b) electric potential \(\displaystyle V = \frac {Q}{4 \pi \varepsilon _0 r}\) at a distance r from a point charge; changes in electric potential

(c) capacitance \(\displaystyle C = 4 \pi \varepsilon _0 R\) for an isolated sphere

(d) force–distance graph for a point or spherical charge; work done is area under graph

(e) electric potential energy \(\displaystyle = Vq = \frac {Qq} {4 \pi \varepsilon _0 r}\) at a distance \(\displaystyle r\) from a point charge \(\displaystyle Q\).

**6.3 Electromagnetism**

This section provides knowledge and understanding of magnetic fields, motion of charged particles in magnetic fields, Lenz’s law and Faraday’s law. The application of Faraday’s law may be used to demonstrate how science has benefited society with important devices such as generators and transformers. Transformers are used in the transmission of electrical energy using the national grid and are an integral part of many electrical devices in our homes. The application of Lenz’s law allows discussion of the use of scientific knowledge to present a scientific argument (HSW1,2,3,5,6,7,8,9,11,12).

**6.3.1 Magnetic fields**

(a) magnetic fields are due to moving charges or permanent magnets

(b) magnetic field lines to map magnetic fields

(c) magnetic field patterns for a long straight current-carrying conductor, a flat coil and a long solenoid

(d) Fleming’s left-hand rule

(e) (i) force on a current-carrying conductor;

\(\displaystyle F = BIL \text{sin} \theta\)

(ii) techniques and procedures used to determine the uniform magnetic flux density between the poles of a magnet using a current-carrying wire and digital balance

(f) magnetic flux density; the unit tesla.

**6.3.2 Motion of charged particles**

(a) force on a charged particle travelling at right angles to a uniform magnetic field; \(\displaystyle F = BQv\)

(b) charged particles moving in a uniform magnetic field; circular orbits of charged particles in a uniform magnetic field

(c) charged particles moving in a region occupied by both electric and magnetic fields; velocity selector.

**6.3.3 Electromagnetism**

(a) magnetic flux \(\displaystyle \phi\); the unit weber; \(\displaystyle \phi = BA \text{cos} \theta\)

(b) magnetic flux linkage

(c) Faraday’s law of electromagnetic induction and Lenz’s law

(d) (i) e.m.f. = − rate of change of magnetic flux linkage; \(\displaystyle \varepsilon = - \frac {\Delta(N \phi )}{\Delta t}\)

(ii) techniques and procedures used to investigate magnetic flux using search coils

(e) simple a.c. generator

(f) (i) simple laminated iron-cored transformer; \(\displaystyle \frac {n_s}{n_p} = \frac {V_s}{V_p} = \frac {I_p}{I_s}\) for an ideal transformer

(ii) techniques and procedures used to investigate transformers.

*Physics Review*, a magazine published for AS and A level students by the University of York and Philip Allan, contains much useful background, examination technique advice and further explanatory material on this and other subject areas covered by this specification. Their website contains more information on how to access past articles and how to subscribe to the publication.

### Exercise 1

## Thinking Conceptually

### Overview

**Approaches to teaching the content**

**6.2 Electric Fields**

Many students of school Physics recall demonstrations of electric fields long after their course of study has ended, and there can be no doubt that this area of Physics is one of the most rich for imaginative experiments and demonstrations that capture the ‘wow’ factor.

Simple demonstration of electric field phenomena such as bending a stream of water by a charged rod, picking up small light objects using a charged rod, the gold leaf electroscope and, of course, the van de Graaf generator are an ideal place to start. The concept of ‘action at a distance’, where no contact is required for a force to be exerted, is a key part of such experiments, which should lead the Learner to the concept of a ‘force field’, or more simply a ‘field’. The requirement for a charged object to be present for a force to be exerted quickly follows, and so the Learner should now be aware of the concept of an electric field existing around a charged object.

Charged objects come in many shapes and sizes, but the visualisation and mathematics of electric fields are made much simpler if a charged object is considered to be a point charge, with the charge concentrated at that point. This is a very reasonable assumption if the distances between objects is large compared to the sizes of the objects themselves, and a similar approach is adopted in the study of gravitational fields.

Charged objects experience a force in an electric field. Physicists represent forces by vector lines – the arrows show the direction of the force experienced by a small positively charged object, and the density of the lines show the strength of the force. Field strength can expressed mathematically as force per unit charge – learners will assume that larger charges result in larger forces, and so some way of expressing force for a standard charge is required for comparison purposes.

The two Laws of Electrostatics are very widely known – ‘likes repel’ and ‘opposites attract’. But inquisitive Learners will want to know how strongly, and over what sort of distance? Coulomb investigated this in the eighteenth century, and in 1785 published his famous Law. It was very similar to Newton’s Law of Gravitation in that it included the product of two quantities (in Coulomb’s case the charges on two objects) divided by the square of the distance between them, and there was a constant (the permittivity of free space, \(\displaystyle \varepsilon_0\)) to describe the effect on the force caused by the intervening material. Coulomb’s Law is a simple inverse-square law that students need to be confident with, and correct manipulation of the equation and the use of the proper units need to become a reliable part of the Learner’s Physics armoury.

If one of the charges involved was a unit charge, then \(\displaystyle E = \frac F Q\) can be combined with Coulomb’s Law to give an alternative expression for electric field strength, namely \(\displaystyle E = \frac {Q} {4 \pi \varepsilon _0R^2}\). Electric field strength is therefore measured in \(\displaystyle N\text { }C^{-1}\).

An electric field between two parallel plates at different potentials is a simple way of investigating a uniform electric field. The shuttling ball experiment is an excellent way of showing that a force is exerted on the charged ball, and the strength of that field (and the frequency of shuttling) can be demonstrated to depend on the voltage difference between the plates and the inverse of the distance between them.

Learners will now be able to express electric field strength as volts per metre, \(\displaystyle E = \frac {V}{d}\). The lines of equipotential in such a uniform field are straightforward to plot using simple apparatus, such as two metal plates, a sandwich made of conducting paper, carbon paper and normal paper and a voltage probe.

Two parallel plates at different potentials can also be regarded as a capacitor, where the charge that can be stored depends on the area A of the plates, the distance d between them and the permittivity \(\displaystyle \varepsilon\) of the dielectric material between them. This links well to the unit on capacitors, and Learners should make the link between the two areas of study.

The capacitance \(\displaystyle C\) of the capacitor is given by \(\displaystyle \ C = \frac {\varepsilon A}{d}\), where \(\displaystyle \varepsilon = \varepsilon_r \varepsilon _0\). The concept of permittivity (where \(\displaystyle \varepsilon_r\) is the relative permittivity of the actual material used and \(\displaystyle \varepsilon_0\) is the permittivity of free space) is an important one – it is usually impractical to produce a useful capacitor with free space between the plates, and disassembly of a barrel-type capacitor will show the Learner that an insulating dielectric material is sandwiched between the plates that allows the electric field to remain without leaking away.

Learners will be aware that charged particles will be affected by an electric field, and the convention that the field lines describe the force acting on a small positive charge will be useful in predicting what will happen to charged particles in a uniform electric field. They should also be able to predict the path of charged particles that enter a uniform electric field if the velocity and field are perpendicular to one another. If the charged particle experiences a constant force due to the electric field perpendicular to its velocity, it will trace out a parabola. This is similar to a particle with constant horizontal velocity in a gravitational field experiencing a force perpendicular to the velocity, hence a parabola. It is perfectly reasonable to expect SUVAT type problems when analysing the motion of charged particles in an electric field.

The definition of electric potential is important. When a charge moves with or against an electric field gradient, energy is transferred and therefore work is done. The work done per unit charge is the electric potential. The reference point is infinity, where the electric potential is defined to be zero. Learners need to be clear on these definitions.

The electric potential \(\displaystyle V\) is found using the equation \(\displaystyle V = \frac {Q}{4 \pi \varepsilon _0r}\), and is large near to a positive charge, and falls away as the distance to the charge is increased. The rate of change of \(\displaystyle V\) with \(\displaystyle r\) is the electric field strength \(\displaystyle E\). Learners often mistake electric potential as having an inverse square relationship with \(\displaystyle r\), rather than the correct simple inverse proportionality, and care should be taken to ensure that they are clear about the nature of \(\displaystyle F\), \(\displaystyle V\) and \(\displaystyle E\).

Learners are likely to be able to understand the idea of an isolated spherical capacitor storing energy by reference to the charged dome on a van de Graaf generator, and calculation of its capacitance \(\displaystyle C\) is relatively simple as long as its radius \(\displaystyle R\) is known.

A plot of force against distance using Coulomb’s Law for a point or spherical charge will result in a characteristically shaped graph. The area under the graph between two points on the distance axis, which is equal to force x distance, is of course equal to the work done in moving the charge between those two points.

The final point is electrical potential energy, which is analogous to gravitational potential energy in a gravitational field, the concept of which should be familiar to Learners from earlier study or from a study of Gravitational Fields. Energy \(\displaystyle = Vq\) (Learners should verify that this is dimensionally correct), and so Electric Potential Energy \(\displaystyle E = Vq = \frac {Qq}{4 \pi \varepsilon _0R}\) for a charge \(\displaystyle q\) at a distance \(\displaystyle r\) from another point charge \(\displaystyle Q\).

**6.3 Electromagnetism**

Most Learners will have made a simple electromagnet earlier in their school careers, usually out of a length of wire wrapped around a cardboard tube, with an iron nail as a core. They will also probably be familiar with a permanent magnet, although they are unlikely to understand what permanent magnetism is. Plotting the magnetic field pattern of a permanent magnet using iron filings is an excellent introduction to magnetism, as it is an excellent method to visualise field lines that have been used in the study of electric and gravitational fields. The more dense the lines, the stronger the field.

Oersted first reported in 1820 that a compass needle deflected when a current was carried by a wire in the vicinity of the compass. Replication of this demonstration will enable the Learner to link electricity and magnetism, which is crucial to the rest of this section.

The magnetic field patterns around a long straight current-carrying conductor can be experimentally demonstrated using compasses, and the right-hand rule gives a useful way of remembering the direction of the field lines. A similar investigation of a flat coil, followed by a solenoid, is recommended as a visualisation tool. Learners often find the concept of a ‘solenoid’ difficult, and appearance of the word ‘solenoid’ in an examination question can cause undue concern. Learners need not be concerned, as a ‘solenoid’ is merely a coil of wire made up of many flat coils together.

Demonstration of a \(\displaystyle F = BIL\) force, using a current-carrying conductor (such as a piece of aluminium foil) in a strong magnetic field, is a highly effective way of introducing the concept of the force acting on a current-carrying wire in a magnetic field. Using a higher current produces a bigger deflection, as does using a stronger magnet and putting more foil in the magnetic field, and so Learners can see the equation \(\displaystyle F = BIL\) at work. Many outside the Physics classroom have heard of Fleming’s Left Hand Rule to predict the direction of \(\displaystyle F\), and proving that it works is a very useful laboratory experience, but the difference between conventional current direction and actual electron flow can trip up the unwary!

The measurement of \(\displaystyle B\) using a current balance is an experiment that will test and reinforce the Learner’s understanding of \(\displaystyle F = BIL\) and Fleming’s Left Hand Rule. It is highly recommended to compare the value of \(\displaystyle B\) obtained using a current balance with that obtained from direct measurement with a Hall probe, and reasonably close agreement can be expected if the experiment is done carefully.

The concept of magnetic flux density, measured in Teslas, is one that Learners find to be relatively straightforward, especially if they have visualised the magnetic field patterns from different strength permanent magnets using iron filings. However, the Tesla itself is a very large unit, and Learners will need to be confident with handling flux densities in the millitesla \(\displaystyle (\text{mT})\) and microtesla \(\displaystyle (\mu \text{T})\) ranges.

Once the Learner is confident with dealing with the interaction of charge carriers moving in wires with a magnetic field, then it is time to remove the constraint of the wire and let the charged particles move freely. The resulting circular path of the charged particles can be demonstrated using an electron beam tube and two Helmholtz coils, and if the Helmholtz coils are not connected, then a permanent magnet can be used to affect the path of the particles. Learners can then visualise the force acting on the charged particles as being at right angles to their motion, and so the circular path is easily explained. The equation \(\displaystyle F = Bqv\) follows from such a demonstration, and the equation for circular motion \(\displaystyle (F = \frac {mv^2} {r})\) can be combined with \(\displaystyle F = Bqv\) to provide expressions for the radius of the path followed by charged particles of a certain mass to charge ratio \(\displaystyle \frac m q )\).

If a charged particle moves through both an electric and a magnetic field, then students should treat the forces acting from each field separately to begin with. The force acting from the electric field is \(\displaystyle F_E = qE\), and that from the magnetic field is \(\displaystyle F_B = Bqv\). If either or both the \(\displaystyle E\) and \(\displaystyle B\) field magnitudes are adjusted until \(\displaystyle F_E\) is equal to \(\displaystyle F_B\), then it is easy to show that \(\displaystyle Bqv = qE\), and so \(\displaystyle v = \frac E Bz\). This is a velocity selector, and is very useful in the study of ions in mass spectrometry, since all ions entering the mass spectrometer must have the same velocity in order for the instrument to yield useful data.

The areas of magnetic flux and magnetic flux linkage can seem to Learners (and their teachers) to be conceptually rather difficult. This need not be so, and the ability to differentiate between the terms magnetic flux, magnetic flux density and magnetic flux linkage is crucial to a full understanding of the area of electromagnetism, Lenz’s Law, Faraday’s Law of Electromagnetic Induction, the operation of a.c. generators and how and why transformers work. This part of the subject material can also appear to the Learner to contain some difficult mathematics, but it does not as long as the symbols used are carefully explained.

If magnetic flux density \(\displaystyle B\) is thought of as the number of lines of flux per unit volume, then magnetic flux is simply the total number of lines of flux. Its symbol is \(\displaystyle \phi\), and it is defined as the product of the magnetic flux density and the area normal to the lines of flux, and is measured in Webers, \(\displaystyle Wb\).

If the coil of wire is at an angle \(\displaystyle \theta\) to the lines of flux, then it can be shown that \(\displaystyle \phi\) is equal to BAsin\(\displaystyle \theta\). The Learner should be able to show that 1Wb = 1Tm^{-2} from a dimensional analysis of this equation.

As its name suggests, magnetic flux linkage occurs when there are many coils in the magnetic field and the contribution from each coil is simply summed together. Hence the equation \(\displaystyle N \phi = BAN\). In this case when there are a number of turns we call it flux linkage and the unit is therefore Weber turns.

Faraday’s Law relates the e.m.f. induced by moving a coil in a magnetic field to the magnetic flux linkage – the faster the coil moves through the magnetic field, the more lines of flux are cut and the larger the induced e.m.f. will be. This needs to be demonstrated in the laboratory for Learners to fully understand it, but it is a simple demonstration.

Lenz’s Law can be effectively demonstrated by dropping a small but powerful magnet through a copper tube and measuring the time taken to fall through it. A word definition of Lenz’s Law follows from observing such a demonstration, and a combination of Faraday’s Law and Lenz’s Law produces \(\displaystyle E = - \frac {d (BAN)}{dt}\), where Lenz’s Law explains the negative sign. If Lenz’s Law were not true, then the Learner should be invited to consider the consequences in terms of energy conservation.

Faraday’s Law is best expressed in words as well as equation form, since not all Physics Learners study advanced mathematics courses. Faraday’s Law can also be used to explain the use of search (or exploring) coils in the measurement of magnetic flux, and as long as a known magnetic field is available for calibration purposes, students can make their own search coils using a simple solenoid and a sensitive ammeter, and then evaluate them.

Once Faraday’s Law is learned, then the a.c. generator can be studied and understood. Generation and transmission of electrical energy in the form of alternating current is a cornerstone of 21st century society, and most Learners will find it difficult to imagine life without mains electricity. This section builds upon earlier learning in that Learners should be aware of the use of a generator at the end of the energy transfer sequence in all methods of electrical energy generation (apart from solar energy), and the Learner can now use their knowledge of Faraday’s Laws to explain the principles behind and the operation of a simple a..c. generator.

As Learners will be aware, a complex system of cables and transformers carry electricity from the generation source into schools, homes and workplaces, but it is a process with several intermediate stages. Successful low loss transmission over long distances requires the use of step-up and step-down transformers, and this unit of study ends with an examination of how transformers work. Learners will be able to use their knowledge of Faraday’s Law to study the induction of an alternating magnetic field by an alternating current in the primary coil, and the reverse process in the secondary coil.

Reference to the Law of Conservation of Energy and Faraday’s Law will assist learning of the Transformer Rules, and understanding the role of low resistance windings and a soft iron laminated core in the reduction of energy losses will follow. Learners should build their own transformers to demonstrate their function, and they can investigate the performance of transformers by changing some design parameters and measuring the input and output potentials and currents.

In this unit, the Learner covers a lot of material, but develops a deeper understanding of electrical and magnetic phenomena, and how these can be understood using relatively simple ideas. This specification provides a very firm foundation for higher Physics study in these areas, and the successful Learner will be very well equipped for the study of electromagnetics and other field-based phenomena.

**Common misconceptions or difficulties students may have, such as confusion between electric and magnetic field effects.**

Electric field effects and magnetic field effects can be easily confused. Electric field effects arise from the interaction of a charged particle with the electric field associated with another charged object. Magnetic field effects arise due to the interaction of a magnetic dipole with the magnetic field associated with a permanent magnet or an electromagnet. Moving charged particles will interact with both types of field, but a stationary charged particle will not interact with an unchanging magnetic field, whereas it will with an electric field.

Electric charge can be either positive (+) or negative (-). Magnetic poles can be north-seeking (N) or south-seeking (S). A magnetic pole should not be referred to as ‘+’ or ‘-’. Isolated charges, positive or negative, can exist, but an isolated magnetic pole cannot exist by itself.

Fleming’s Left Hand Rule is conceptually simple, but Learners need to be able to correctly state which quantity is represented by the thumb and first two fingers, and to remember that conventional current flow is in the opposite direction to electron flow.

Learners may confuse the Earth’s gravitational field and its magnetic field, and may seek to explain observed phenomena in terms of the wrong field model. Care should be taken to ensure that such misconceptions are addressed as soon as possible.

Learners can be confused by the similar-sounding terms *magnetic flux*, *magnetic flux density* and *magnetic flux linkage*. Care needs to be taken that the Learner is able to correctly define and use these terms.

The correct definition and application of Lenz’s Law can cause difficulties among less-confident Learners, and time should be spent to ensure that Learners can recall and apply Lenz’s Law in simple situations.

Some students may find the mathematical treatment of inverse square laws to be difficult on first sight, and the concept of rate of change of magnetic flux linkage in Faraday’s Law may also be of concern. This specification does not require students to be able to carry out differentiation or integration processes in a quantitative manner, although word-based qualitative descriptions of factors that can alter the rate of change may be required.

Learners need to be able to apply the Law of Conservation of Energy to transformer calculations, and remember that the secondary coil output power can never exceed the primary coil input power.

**Conceptual links to other areas of the specification – useful ways to approach this topic to set students up for topics later in the course.
e.g. links to energy and kinematics**

There are great similarities between gravitational, electric and magnetic fields, and the common inverse square nature of the Laws that govern all of them make the mathematics of these areas much simpler.

The principles of circular motion are essential to an understanding of the circular paths followed by charged particles in magnetic fields.

The concept of charge and current is linked to other Modules within this specification (Physics A AS Module 4) as well as to several PAGs.

*Physics Review*, published by the University of York and Philip Allan, contains much information of use to A level Physics students. Articles range from full descriptions of topic areas to providing advice on learning to successfully tackle the mathematical aspects of Physics study. A full listing of past articles may be found here.

The School Science Review, published by the Association for Science Education, contains articles of use to teachers and learners. More details on how access the journal and previous articles may be found here.

Oxford University Press is OCR’s Resource Partner for the new specifications covered by this Delivery Guide, and resources are detailed on their website as they are published and become available. The website address is here.

Learners may wish to learn more about the links between electricity and magnetism, especially in the formulation of electromagnetic theory. The brilliant work of James Clark Maxwell should be studied by all aspiring university physicists, and a good starting point is chapter 8 of ‘The Man Who Changed Everything – The Life of James Clerk Maxwell’, by Basil Mahon, Wiley, 2003 (ISBN 0-470-86171-1).

## Thinking Contextually

### Overview

This subject area is rich in experiments and demonstrations, and a good place to start is with simple electrostatics. Once the idea of an electric field around a charged object, and the effect that it can have on other objects, is accepted by Learners, then the van de Graaf generator can be used to take the concept a lot further. This is likely to be one of the most memorable experiments from the entire Physics course, and there are many ways in which electric fields, discharges and the Laws of Electrostatics can be experienced and demonstrated (in a safe manner, of course).

Following this, experiments to observe electric field patterns should be undertaken – these will show that electric fields have lines of force too. The shuttling ball experiment will show the force acting on a charged sphere in an electric field, and will lead to a discussion about the nature of electric current in terms of charge carriers.

The concept of a line of equipotential can be investigated using a simple experiment where voltages relative to ground are plotted using conductive paper with carbon paper on top of it. The potential near a charged sphere can be investigated with a flame detector – this is a memorable experiment, if sometimes a little tricky to set up.

Simulations are a good and simple way of visualising fields and their effects on charged objects, and the learner should make good use of them inside and outside the classroom. They can be very effective when used alongside experimental activities to show the reasons for the observations made by learners.

The area of electric fields overlaps with that of the study of capacitors, and the design of the parallel plate capacitor can be investigated by making some simple examples using different dielectric materials. The concept of charge storage by an isolated spherical capacitor will be made much easier if the dome of a van de Graaf generator is used as a model, since it is very clear that there is charge (and therefore energy) stored before it is discharged.

A study of electromagnetism should start with a study of the magnetic field round a permanent magnet using iron filings. This is one of the easiest and most effective ways of visualising a field. The field patterns around current carrying conductors, as a straight wire, flat coil and long coil solenoid will enable to Learner to link electricity and magnetism together. Oersted’s simple experiment showing that an electric current produces a magnetic field is a good way of introducing this link.

Demonstration of a \(\displaystyle F = BIL\) force using a low weight conductor (e.g. a thin strip of aluminium foil) will lead the Learner to Fleming’s Left Hand Rule, although care needs to be taken when describing the direction of current flow, as learners can often be confused between conventional current flow and actual electron movement. The current balance is based on \(\displaystyle F = BIL\), and Learners should carry out the experiment to measure \(\displaystyle F\) and compare it with prediction.

Building electric motors is a good way to reinforce the learning, and explaining how they work is a good project-based task that will interest even the most reluctant learner. Building a working motor can also be a good test of patience and practical skill, which will stand the Learner in good stead for future study.

Once the Learner is comfortable with the concept of a force acting on electrons in a wire, the next step is to take the wire away and see what happens to a flow of charged particles when they move through a perpendicular magnetic field. The electron beam tube is an ideal demonstration of the circular motion shown by charged particles, and using a strong permanent magnet (with care!) can also change the path of the particles.

The concept of a velocity selector is fairly straightforward if the electric and magnetic field strengths are adjusted so that the same force is produced – Learners should find the \(\displaystyle v = \frac E B\) very simple after considering the equations involved.

Faraday’s Law could be introduced by viewing a simulation, and then trying an experiment – this is a particularly good area for Learners to employ fast data logging methods to obtain useful data. Demonstrations of Lenz’s Law using a falling magnet is likely to see Learners struggle at first to explain their observations, but gentle encouragement should see them explain the reduced rate of falling using the correct ideas.

Learners can compare their calculation of the magnetic flux density of a permanent magnet using a small search coil with the result obtained from a Hall probe – this will enable them to become familiar with Faraday’s Law and its use.

The a.c. generator can be introduced as a motor in reverse, and it can be investigated as such with a falling weight to drive the coil.

The section ends with a study of transformers. It is strongly suggested that Learners start their investigation of transformers using prepared examples, and then move on to make their own. The effect of changing the number of coils on primary and secondary can easily be evaluated, and changing of other transformer parameters, such as using high resistance windings and using a non-laminated core, should also be done to show the reasons behind the design and construction of modern transformers.

The Learner’s journey starts with a simple stationary electrostatic charge, and ends with the efficient transmission of mains electricity. The quality and comfort of 21st century life depends on the phenomena investigated in this unit, and the Learner is able to appreciate the simplicity and genius of the scientists who developed these ideas and devices through participating in very similar experiments to those described by Oersted, Faraday, Coulomb and Lenz.

### Electric fields, electrostatic phenomena and electrostatic effects

An introduction to electric fields can be found at

**Institute of Physics**

Preparation for electric fields topic.

Introductory experiments on electrostatic phenomena can be found at:

**Nuffield Foundation**

Electrostatic charges.

The safe use of the Van der Graaf generator to demonstrate electrostatic effects in the school laboratory is described at:

**Nuffield Foundation**

Van de Graaff generator safety

### Experiments into electric fields

Visualisation of an electric field by experiment, using semolina, is described at:

**Nuffield Foundation**

Electric fields 1.

More electric fields experiments are outlined at:

**Nuffield Foundation**

Electric fields 2.

### Plotting equipotentials, modelling current flow and observing the force acting on a charged object in an electric field

Plotting lines of equipotential in a uniform field is shown on the document 'Plotting equipotentials' from the Institute of Physics.

The shuttling ball experiment is an effective way of modelling current flow as well as observing the force acting on a charged object in an electric field. It is described in a video on YouTube entitled 'The mysterious shuttling ball physics experiment'. Laboratory instructions may be found at:

**Nuffield Foundation**

Forces in an electrostatic field

### Isolated sphere capacitor

### Gravitational fields and radial electric fields

There is a useful comparison of gravitational fields from the Institute of Physics (see link 'Uniform electric fields').

The visualisation of radial electric fields may be helped by the material on the schoolphysics website (see link 'Radial electric field').

### Simulations of phenomena involving electric fields

Simulations of various phenomena involving electric fields may be found at may be found at:

**PhET Interactive Simulations (University of Colorado)**

Capacitor lab

Use of these simulations is highly recommended for out of classroom learning and for preparation for subsequent experimental work.

### Plotting the magnetic field of a permanent magnet

Guidance for plotting the magnetic field of a permanent magnet can be found at:

**Institute of Physics**

Describing magnetic fields.

This can then be developed to plotting field patterns around current-carrying wires, flat coils and long coil solenoids using material at:

**Nuffield Foundation**

Magnetic field due to a long close-wound coil

### Force on a current carrying conductor

The force on a current-carrying conductor can be investigated using:

**Institute of Physics**

The force on a conductor in a magnetic field

**Nuffield Foundation**

Magnetic fields due to currents in wires.

The current balance experiment is described at:

**Nuffield Foundation**

The current balance

Making and operation of simple electric motors is given at:

**Institute of Physics**

Electric motors.

### Electron beam tube demonstration

The electron beam tube demonstration is given at:

**Institute of Physics**

The force of a moving charge.

### Electromagnetic induction using a moving wire in a magnetic field

Electromagnetic induction using a moving wire in a magnetic field is described at:

**Institute of Physics**

Electromagnetic induction

**Nuffield Foundation**

Cutting a magnetic field with a wire

A data logging experiment involving a falling magnet through a coil is given at:

**Nuffield Foundation**

Datalogging electromagnetic induction

### Lenz's law

Lenz's law can be observed in action using a falling magnet in a copper tube and two descriptions are given at:

**Institute of Physics**

Rates of change

**Nuffield Foundation**

Electromagnetic braking of a copper pipe

Eddy currents arising from Lenz's law can be investigated using methods given at

**Institute of Physic**

**s**

Further eddy current demonstrations

### Electric generators as motors in reverse

Electric generators as motors in reverse are described at:

**Institute of Physics**

Electric motors

**Nuffield Foundation**

An electric motor used as a generator

### Transformer experiments

Transformer experiments are described at:

**Nuffield Foundation**

Transformers

**Institute of Physics**

Transformers (TAP)

### Simulations of electromagnetic phenomena

Simulations of many electromagnetic phenomena can be found at:

**PhET (University of Colorado)**

Magnets and electromagnets

### Aurora Borealis and Aurora Australis

Finally, source material for a possible research activity into the Aurora Borealis and Aurora Australis may be found at:

**Northern Lights Centre**

Northern Lights

**Science Kids**

Fun aurora facts for kids

Learners should be encouraged to find out how the interaction of the Earth’s magnetic field with streams of charged particles from the Sun is responsible for the survival of much of the life on Earth.

### Investigating factors affecting the capacitance of a capacitor

### Investigating transformers

### Determining the magnetic field strength of a magnet

## Acknowledgements

### Overview

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