To give some further insight into the AmpÃ¨reâ€“Maxwell law, we will now consider two situations where it plays a significant role.

Author(s): The Open University

We need to generalise AmpÃ¨re'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 AmpÃ¨re's law. The modified equation then reads

What can b
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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
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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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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
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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
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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
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Eventually, movement along faults initiated during the continental rifting stage ceases, and the entire continental margin starts to subside. Subsidence at this stage occurs because of lithospheric cooling as the distance between the margin and spreading ridge-axis increases, rather than as a result of tectonic movement of the fault blocks (as during the continental rifting stage). By now, all tectonic activity is focused at the new oceanic spreading axis and the continental lithosphere can b
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Think again about the value for the total volume of water stored on Earth: 1460 000 000 km3.

When dealing with large numbers such as one thousand four hundred and sixty million (1460 000 000), it is tedious to write the number in words or to keep writing all of those zeros. Worse still, it is very easy to lose some of the zeros or add extra ones by mistake. Fortunately, large numbers can be referred to without having to write out all of the zeros. The powers of ten not
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The psychological arena is hugely complex because there are additional issues of responsibility and treatment. Briefly, society takes a more lenient attitude towards the behaviour of someone who is ill (diseased) compared to someone who is well. The diseased person is not fully responsible for their actions (â€˜They can't help itâ€™). Therefore any individual with antisocial (aggressive) behaviour who is diagnosed as having a disease is largely absolved of blame. Having a disease, means, at l
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Particular nerves, such as those sensory nerves that arise from the nasal retina (the side of the retina adjacent to the nose), cross the midline; other sensory nerves, such as those that arise from the temporal retina do not. This pattern is consistent between individuals, to such an extent that a map of the nervous system is good enough to be used to locate a particular nerve pathway in most people. (See Author(s): The Open University

As well as affecting behaviour (Section 3.4) neonatal testosterone also affects the physical characteristics of some areas of the brain. One of these is a small area of the hypothalamus, the medial preoptic area, which, although small, is much larger in males than in females. This size difference is mediated by testosterone.

<
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The main role of vitamin D is to facilitate the uptake of calcium from food, through the lining of the small intestine into the blood. It also controls the deposition of calcium in the bones during growth and maintains adult bone structure. If vitamin D is deficient, with less calcium available, the skeleton fails to develop normally. The most obvious symptom is the bowing of the leg bones in children, producing the condition called rickets (Author(s): The Open University

## Activity 4

Look back at Table 1 and identify the foods that contain vitamin A. On the basis of this information, try to predict where vitamin A is stored in the human body.

### 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

Before the 19th century, one of the hazards of long sea voyages was a condition called scurvy, whose symptoms were loss of hair and teeth, bleeding gums, very slow healing of wounds, and eventually death. Hundreds of sailors and explorers died from scurvy until a Scottish physician, James Lind, in the 1750s discovered that adding a daily portion of citrus fruit to the rations of those at sea could prevent the condition, whereas adding cider, vinegar or various other substances that he tested,
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After studying this Unit you should know:

• that certain minerals are required in the body and that some minerals form essential structural components of tissues;

• that sodium, potassium, calcium and chloride ions are important in maintaining the correct composition of cells and of the tissue fluids around them (homeostasis);

• that some minerals are essential components of important molecules such as hormones and enzymes;

• that the correct
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Both vitamins and minerals are essential in the diet in small quantities.The term â€˜vitaminâ€™ was not coined until early in the 20th century, to describe those chemicals in food without which a pattern of deficiency symptoms (often called a deficiency syndrome) occurs. Minerals, also called mineral elements, are those elements other than carbon, hydrogen, oxygen and nitrogen that are found in the body.

This unit looks at the two main groups of vitamins: the fat-soluble vitamins A, D,
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In this unit you have found out that:

• The sensation of pain is caused by the release of a chemical (prostaglandin) that stimulates the nerve endings and sends an electrical message to the brain.

• Pain can be reduced if the formation of prostaglandin can be inhibited.

• Prostaglandin is formed, from arachidonic acid, in a cavity in the active site of the enzyme cyclooxygenase (COX).

• Geometrical isomerism
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