In order to analyse the limitations of AmpÃ¨re's law, and suggest ways of overcoming them, we need to use some properties of divergence. For ease of reference, these properties are given below:

### Some properties of divergence

1. The divergence of any curl is equal
Author(s): The Open University

The conservation of charge is a basic tenet of electromagnetism. It can be simply expressed by the equation

where Qtot is the total charge in the Universe. However, such an equation does not really help us very much, because we are not usually concerne
Author(s): The Open University

This unit presents Maxwell's greatest triumph â€“ the prediction that electromagnetic waves can propagate vast distances through empty space and the realisation that light is itself an electromagnetic wave. Visible light has a very narrow range of wavelengths, but this tells us more about the sensitivity of our eyes than about the nature of electromagnetic radiation. A few years after Maxwell's death other types of electromagnetic radiation, including radio waves, X-rays and gamma rays, were
Author(s): The Open University

By the end of this unit you should be able to:

• explain the meaning of the emboldened terms and symbols, and use them appropriately;

• state the equation of continuity and use it in simple problems;

• state the conditions under which AmpÃ¨re's law is true and explain why it does not apply more generally;

• state the AmpÃ¨reâ€“Maxwell law and explain why it has a greater domain of validity than AmpÃ¨re's law;

• state and name the
Author(s): The Open University

James Clerk Maxwell produced a unified theory of the electromagnetic field and used it to show that light is a type of electromagnetic wave. This prediction dates from the early 1860s when Maxwell was at King's College, London. Shortly afterwards Maxwell decided to retire to his family estate in Galloway in order to concentrate on research, unhindered by other duties. He was lured out of retirement in 1871, when he became the first professor of experimental physics in the Cavendish Laboratory
Author(s): The Open University

The content acknowledged below is Proprietary (see terms and conditions). This content is made available under a Creative Commons Attribution-NonCommercial-ShareAlike 2.0 Licence

Grateful acknowledgement is made to the following sources for permission to reproduce material in this unit:

## Author(s): The Open UniversityLicense informationRelated contentExcept for third party materials and/or otherwise stated (see terms and conditions) the content in OpenLearn is released for use under the terms of the Creative Commons Attribution-NonCommercial-Share

Altmann, P., Cunningham, J., Dhanesha, U., Ballard, M., Thompson, J. and Marsh, F. (1999) â€˜Disturbance of cerebral function in people exposed to drinking water contaminated with aluminium sulphate: retrospective study of the Camelford water incidentâ€™, British Medical Journal, vol. 319, pp. 807â€“811.
Bank, M. S., Crocker, J. B., Davis, S., Brotherton, D. K., Cook, R., Behler, J. and Connery, B. (2006) â€˜P
Author(s): The Open University

Knowing the equation allows you to perform several useful calculations without needing to make a graph, and we'll look at one such example in a moment.

Bacteria are single-celled organisms. Many different types of bacteria exist and they populate almost every environment on earth, from deep oceans to soil to human intestines. Several bacteria are beneficial to us: for instance, our gut bacteria can help to break down foodstuffs that we would otherwise find difficult to digest. However, some bacteria produce harmful toxins and if they grow in an uncontrolled way in our bodies this can have serious health consequences.

If a bacterium is
Author(s): The Open University

Many natural processes involve repeated doublings or halving at regular intervals. You may have come across this already in your work, in the context of bacterial growth or radioactivity. In this section, we are going to look in more detail at bacterial growth and radioactivity and we will be using graphs to examine how the numbers of bacteria or numbers of radioactive atoms change over time.

Author(s): The Open University

To illustrate how to create and use line graphs, we will use the example of a calibration curve.

A calibration curve is a type of line graph in which the response of a measuring device to a series of known concentrations of a substance is plotted. You can then make a measurement of an unknown sample â€“ in the case we're about to examine, blood serum samples from new-born infants â€“ and use the calibration curve to work out what concentration of substance is present.

Author(s): The Open University

It's important to choose a scale that covers the range of values you have recorded for that particular axis. If the scale is too big, then all of your measurements will be bunched up at one end of the graph, making it difficult to read. It is also very important to keep the scale consistent all along the axis, i.e. don't suddenly change the spacing between the units of measurement on an axis.

Author(s): The Open University

Suppose you have less than one of any particular unit: how would you represent that using the decimal system?

Well, we've already seen that decimal numbers rely on a positional system, in which values get smaller by factors of ten as you read from left to right. If we continue doing this, then the number to the right of a single unit represents tenths of that unit. A decimal point is then used to mark the boundary between the whole units and tenths of that unit.

For instanc
Author(s): The Open University

Many different systems for writing numbers have been developed over the history of humankind.

The easiest way of counting small numbers is to use your fingers, and for this reason many numerical systems, such as the decimal system, are based around the number ten. But what happens when you run out of fingers to count on?

Numbering systems get round this problem by using a system of scale in which many small units are represented by a single larger unit, and many of these la
Author(s): The Open University

This sample of S110 material is taken from Module 2, entitled Using numbers and handling data. As you read the material, bear in mind that it is taken from a work-based course, designed for those who are employed in the health services, perhaps as a paramedic or as operating theatre staff. If you were a student on the course, you would have an OU tutor to help you, plus a work-based mentor supplied by the employer â€“ normally the NHS. The aim is to use the workplace as a teaching aren
Author(s): The Open University

The content acknowledged below is Proprietary (see terms and conditions). This content is made available under a Creative Commons Attribution-NonCommercial-ShareAlike 2.0 Licence

Grateful acknowledgement is made to the following sources for permission to reproduce material in this unit:

## Author(s): The Open UniversityLicense informationRelated contentExcept for third party materials and/or otherwise stated (see terms and conditions) the content in OpenLearn is released for use under the terms of the Creative Commons Attribution-NonCommercial-Share

Now you have completed this unit, try the following questions to test your understanding of this material.

## Question 19

• A discrete exotic terrane refers to a large crustal fragment that can be recognised by its distinct sedimentary, igneous, metamorphic and structural history compared with that of its eventual neighbours, and has been juxtaposed into position by major strikeâ€“slip faults.

• Nine discrete exotic terranes make up the Basement in the British Isles. These consist primarily of Precambrian metamorphosed rocks but also contain some unmetamorphosed sedi
Author(s): The Open University

In Section 3 we referred to the Caledonian and Variscan Orogenic Belts. These are interpreted as representing past destructive plate margins or more strictly speaking, representing the final phases of ocean closure that resulted in continental collision. Section 4 explores the extent to which it is possible to detect different
Author(s): The Open University

Natural gas, which is largely methane, is burned to provide heat for cooking and domestic heating and as an industrial power source. This process of burning involves the reaction of methane with oxygen in air to produce carbon dioxide and water.

A chemical equation can be constructed for the reaction of methane with oxygen to give carbon dioxide and water as the products.

1. The first step is to write the formulas of the reactants on the left and t
Author(s): The Open University