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4.2 Digesting cellulose

Figure 3 in this section contains a lot of information and many terms that are probably new to you. Set aside the detail for the moment, read
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3.6 The numbers game … or the struggle for existence

In the majority of The Life of Mammals TV sequences there is relatively little evidence of any struggle for existence, apart from the occasional predator/prey interaction. Even then you are offered the comforting reassurance that ‘four out of five chases end with the prey escaping’. So you could be forgiven for thinking that most mammals survive to a ripe old age, or at least until, like the topi, they have fulfilled their reproductive potential. Not so! Four out of five chases may
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Introduction

Sixty-five million years ago, animal and plant life were very different from nowadays, but there were rat-sized placental mammals living successfully on the ground. They were insect eaters, i.e. insectivores, feeding on the vast numbers of insects and other invertebrates living in soil, leaf litter and low-lying vegetation. Insectivore means ‘insect eater’, and in this unit we will explore the world of insect-eating mammals, classified together on the basis of a reasonably close evolution
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7.4 Nuclear abundances as evidence for the big bang

What we have seen is that a theoretical model based on the assumption that there was a big bang, and incorporating an assumption about the present-day value of the baryonic density, ρb,now, leads to definite predictions as to what the nuclear abundances must have been when the elements froze-out. This, therefore, provides us with a third way of checking out the big bang hypothesis: Do the present-day cosmic nuclear abundances agree with these predictions for any plausible v
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7.3 The formation of light nuclei

It is the very high temperatures that make the early stages of the big bang relatively simple to calculate. When it comes to the formation of the first nuclei, we are looking at a temperature that has dropped to about 109 K, this being achieved approximately 3 minutes after the instant of the big bang. For nuclei to form, the temperature must still be high enough that charged nuclei can approach each other closely – despite the electrostatic repulsion between their positive charg
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5.2 The energy of electromagnetic waves

The energy density of an electric field E is

Although we will not prove it in this unit, a very similar result applies to magnetic fields. The energy density of a magnetic field B is

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4 Maxwell's equations

We have reached a major milestone. All four of Maxwell's equations are now in place. This is an appropriate place to review their meaning and significance. We concentrate here on the differential versions, which are as follows:

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3.3.2 A capacitor with time-varying charges on its plates

Figure 4 shows a parallel plate capacitor with circular plates, which is being charged by steady currents flowing along straight wires. We know that there is a circular pattern of magnetic field lines around the wires, but what happens inside the capacitor, between the plates?

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3.3.1 An expanding sphere of charge

First consider an expanding spherically-symmetric ball of positive charge. This is not an implausible state of affairs. If the charges in the distribution are not held in place, their mutual repulsion leads to a spherically-symmetric expansion and a spherically-symmetric outward flow of current. Any spherically-symmetric distribution of current is magnetically silent – that is, it produces no magnetic field. This is true both outside and inside the current distribution. We will now show tha
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3.3 The Ampère–Maxwell law in action

To give some further insight into the Ampère–Maxwell law, we will now consider two situations where it plays a significant role.


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3.2 Generalising Ampère's law

We need to generalise Ampère's law beyond the confines of static charge densities. Let's try adding an extra (and at this stage unknown) vector field, K to the right-hand side of the differential form of Ampère's law. The modified equation then reads

What can b
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3.1 Limitations of Ampère's law

In order to analyse the limitations of Ampère'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
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2 The equation of continuity

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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1 Maxwell's greatest triumph

This unit presents Maxwell's greatest triumph – 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
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Learning outcomes

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 Ampère's law is true and explain why it does not apply more generally;

  • state the Ampère–Maxwell law and explain why it has a greater domain of validity than Ampère's law;

  • state and name the
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Introduction

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
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Acknowledgements

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:

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References

Altmann, P., Cunningham, J., Dhanesha, U., Ballard, M., Thompson, J. and Marsh, F. (1999) ‘Disturbance of cerebral function in people exposed to drinking water contaminated with aluminium sulphate: retrospective study of the Camelford water incident’, British Medical Journal, vol. 319, pp. 807–811.
Bank, M. S., Crocker, J. B., Davis, S., Brotherton, D. K., Cook, R., Behler, J. and Connery, B. (2006) ‘P
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3.6.2 Exponential increase: bacteria

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
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