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 AmpÃ¨reâ€“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

Author(s): The Open University

Finally, our electric and magnetic fields must satisfy the AmpÃ¨reâ€“Maxwell law in empty space. Using Equations 7.21 and 7.23, we obtain

which requires that

Author(s): The Open University

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
Author(s): The Open University

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
Author(s): The Open University

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

Author(s): The Open University

The difficulty with having so much of the Earth's water locked up in the oceans is summed up poetically by Coleridge's â€˜Ancient Marinerâ€™, 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
Author(s): The Open University

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 â€˜blue planetâ€™.

Author(s): The Open University

As you walk down the street one day, you hear a voice from somewhere behind you that seems to be discussing this unit. It says:

â€˜My dad's tutor's no joker, and he told me the TMA's going to hit home with a bang.â€™

You turn to find the face behind the voice, which is a gravelly Glaswegian baritone, but the man has gone, leaving you to ponder what he has said. Let us call his sentence exam
Author(s): The Open University

## Activity 14

What is the condition that results from vitamin C deficiency and what are its symptoms?

You will probably remember from the start of this
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Vitamin B12 is yet another group of compounds, this time with an atom of the metal called cobalt (present in only trace quantities in the body) in their structure, hence the alternative name â€˜cobalaminâ€™. Vitamin B12 works alongside folate and if levels of it are low, folate deficiency symptoms occur too. It is stored in the liver and in general the body does not appear to need a regular intake. Many people have enough B12 stored in their liver to last for
Author(s): The Open University

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
Author(s): The Open University

Niacin, which comprises two compounds, nicotinic acid and nicotinamide, also occurs widely in food and is added to many breakfast cereals. It is easily absorbed into the blood from the digestive system and plays a vital role in energy production in cells. It appears to reduce the levels of low density lipoproteins or LDLs in the blood and increase high density lipoproteins or HDLs, perhaps by affecting the proteins that carry the fats. This is important because LDLs are a way of transporting
Author(s): The Open University

Vitamin B, often called the vitamin B complex, consists of a whole range of different compounds, some of which have similar functions and work together. However, unlike the families of compounds forming vitamins E and K, the B vitamins are sufficiently different from one another to be given individual names or numbers, and to be listed separately on many food labels. Except for vitamin B12, the body can only store limited amounts of B vitamins and because they are all water-soluble
Author(s): The Open University

Like vitamin E, vitamin K is fat-soluble and composed of a series of related compounds. Vitamin K is widely distributed in the diet (see Table 1) and it is absorbed from the small intestine with the assistance of bile acids. Vitamin K is also manufactured by the bacteria that inhabit the human large intestine and appears to be absorbed there too. The main role of vitamin K is in blood clotting. This process requires the presence of a number of different chemicals, called clotting factors, in
Author(s): The Open University

Imagine you have found some old family photograph albums which span many generations. What are the distinctive family features, or characters, that demonstrate the relatedness of individuals? In other words, what characters do they have in common? For example, they might have brown eyes, a white forelock in their hair, ears that are closely attached to the head, that is, without lobes. But you will also notice the striking differences between related individuals. For example, they may differ
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Genes are units of inheritance that contribute to a personâ€™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 â€“ mastering the literature and formulating a research problem and plan.

2. Intensive research â€“ 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.

Author(s): The Open University