The electric and magnetic fields given by Equations 7.21 and 7.23 can satisfy all four of Maxwell's equations in empty space. Gauss's law and the no-monopole law are immediately satisfied because the fields are transverse. Faraday's law and the Ampère–Maxwell law will also be satisfied if we can find electric and magnetic fields that obey Equations 7.24 and 7.26.

We are looking for wave-like solutions, so it is sensible to try

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Finally, our electric and magnetic fields must satisfy the Ampère–Maxwell law in empty space. Using Equations 7.21 and 7.23, we obtain

which requires that

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Substituting Equation 7.23 into the no-monopole law gives immediate agreement because

The no-monopole law is analogous to Gauss's law in empty space, and it leads to a similar conclusion: the magnetic wave must be transverse. This has already been established using Farada
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Substituting Equation 7.21 into Faraday's law gives

This shows that a propagating electric wave is automatically accompanied by a transverse magnetic wave. The magnetic field oscillates in the y-direction, which is perpendicular to the direction of propagation and
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Substituting the assumed form of the electric field (Equation 7.20) into the empty-space version of Gauss's law (Equation 7.16) gives

The first two partial derivatives are equal to zero because f does not depend on x or y. So we obtain

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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
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The difficulty with having so much of the Earth's water locked up in the oceans is summed up poetically by Coleridge's ‘Ancient Mariner’, becalmed on board ship in the doldrums, beneath a blazing Sun.

Water, water, everywhere,

And all the boards did shrink;

Water, water, everywhere,

Nor any drop to drink.

(Samuel Taylor Coleridge, The Rime of the Ancient Mariner, 179
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When astronauts first ventured to the Moon in the late 1960s, they were captivated by a vision of the Earth in colour as it had never been seen before (Figure 2). It is not surprising that, after pictures like this were published, the Earth became known as the ‘blue planet’.

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Now that we have examined the processes involved in understanding a sentence in some detail, we will turn to the issue of how the brain achieves the task. We will begin with the initial capture and analysis of the speech signal.

Vibrations in the air are channelled by the structure of the external ear into the ear canal (Author(s): The Open University

## Question 12

• (a) If two tones are broadcast through headphones at an intensity of 100 dB SPL, which will sound louder, a 100 Hz tone or a 1000 Hz tone? Why?

• (b) How loud must a 100 Hz t
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## Richard P. Feynman (1918–1988)

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Vitamin B6 is composed of pyridoxine and two closely related compounds. It is found in small quantities in many foods, though it can be destroyed in the cooking process. No clear deficiency disease has been recognised in humans as being directly caused by lack of this vitamin, since it is often found in conjunction with other B vitamins and their absence has greater effects. Its main role is in the conversion of some amino acids into other ones, depending on the requirements of the
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Genes are units of inheritance that contribute to a person’s behaviour and health. In this unit you will learn what genes, DNA and chromosomes are and how they combine to make the human genome. You will also learn how the principles of inheritance work, the effect that our genetic make-up has on health, and how genetic material is passed on from generation to generation.

This unit is an adapted extract from the course Author(s): The Open University

The content acknowledged below is Proprietary (see terms and conditions) and is used under licence.

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

## Unit Image

Chase Crowson flickr.com (18 October 2007)

All other materials included in this unit are derived from content originated at the Open University.

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A modern PhD can be viewed as having three key phases (very roughly, but not strictly, corresponding to the three years of a full-time degree), each of which contributes a necessary element of mastery:

1. Orientation – mastering the literature and formulating a research problem and plan.

2. Intensive research – gathering the evidence to support the thesis, whether empirical or theoretical.

3. Entering t
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8 Websites for further information:

For general in
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1.6 Conclusion

This unit has presented an overview of the ways in which organisms living in temperate habitats are adapted to survive the winter. The unit has shown how a limited set of environmental changes associated with the onset of winter can lead to a diversity of adaptations and therefore a large diversity of species.

On the basis of the examples discussed in this unit, we can identify four factors that contribute to the diversity of adaptive strategies for coping with winter.

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1.5.5 Social Bookmarks

If you find you have a long unmanageable list of favourites/bookmarks you might like to try social bookmarks as an alternative.

## Activity - What you need to know about Social Bookmarks

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1.4.2 P is for Presentation

By presentation, we mean, the way in which the information is communicated. You might want to ask yourself:

• Is the language clear and easy to understand?

• Is the information clearly laid out so that it is easy to read?

• Are the fonts large enough and clear?

• Are the colours effective? (e.g. white or yellow on black can be difficult to read)

• If there are graphics or photos, do they help
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1.3.9 Internet resources

There are many websites where you will find useful information on science and nature. With all information on the internet you need to make a judgement on the reliability of the information

 BBC Science and Nature Part of the BBC's website covering various topics on science and the natAuthor(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 Copyright 2009 University of Nottingham