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A treatise on magnetism and electricity Volume 1. N° de ref. de la librería

**Sinopsis:** This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1898 Excerpt: ...depend upon the radius, but yet so far as we have seen may depend upon the position of the spherical surface. This gives the mean value of ff over the sphere. Now let the sphere, without alteration of the radius, be displaced through a small distance dx in the direction of x. The change of the mean potential is 51 that is, dC/dx is the mean value of df/dx taken over the sphere. This vanishes when r is infinite since we suppose the fluid at rest at infinity. Hence dC/dx = 0 also when r is infinite. Similarly dC/dy = 0, dC/dz = 0. But C has the same value for all concentric spheres enclosing the inner bounding surfaces. Consider then two such spheres, one of finite radius, the other so large that df/dx is zero at every point of it, and let them be displaced together. Since dC/dx is zero for the large sphere it is also zero for the smaller. Thus C does not depend on the position of the centre of the sphere, and is the same for every spherical surface enclosing all the inner bounding surfaces. If the sphere considered be wholly situated in the region of irrotational motion the value of M is zero, and we have 52 that is, the average potential over the surface is independent of the radius of the sphere and is the same for all spheres having the same centre. The average potential over any sphere is therefore equal to that over an infinitesimal sphere surrounding the centre; that is, it is equal to the potential at the centre. This theorem is due to Gauss and, with the results which follow, is of great importance in the electrostatic analogue. 305. It follows that the potential cannot be constant over any finite' portion S of the non-rotating fluid without being constant over the remainder. For, taking this not to be the case, imagine a sphere described having its ...

Título: **A treatise on magnetism and electricity ...**

Condición del libro: **Good**

Editorial:
RareBooksClub

ISBN 10: 1236266528
ISBN 13: 9781236266521

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Paperback
Cantidad: 20

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**Descripción **RareBooksClub. Paperback. Estado de conservación: New. This item is printed on demand. Paperback. 164 pages. Dimensions: 9.7in. x 7.4in. x 0.3in.This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1898 Excerpt: . . . depend upon the radius, but yet so far as we have seen may depend upon the position of the spherical surface. This gives the mean value of ff over the sphere. Now let the sphere, without alteration of the radius, be displaced through a small distance dx in the direction of x. The change of the mean potential is 51 that is, dCdx is the mean value of dfdx taken over the sphere. This vanishes when r is infinite since we suppose the fluid at rest at infinity. Hence dCdx 0 also when r is infinite. Similarly dCdy 0, dCdz 0. But C has the same value for all concentric spheres enclosing the inner bounding surfaces. Consider then two such spheres, one of finite radius, the other so large that dfdx is zero at every point of it, and let them be displaced together. Since dCdx is zero for the large sphere it is also zero for the smaller. Thus C does not depend on the position of the centre of the sphere, and is the same for every spherical surface enclosing all the inner bounding surfaces. If the sphere considered be wholly situated in the region of irrotational motion the value of M is zero, and we have 52 that is, the average potential over the surface is independent of the radius of the sphere and is the same for all spheres having the same centre. The average potential over any sphere is therefore equal to that over an infinitesimal sphere surrounding the centre; that is, it is equal to the potential at the centre. This theorem is due to Gauss and, with the results which follow, is of great importance in the electrostatic analogue. 305. It follows that the potential cannot be constant over any finite portion S of the non-rotating fluid without being constant over the remainder. For, taking this not to be the case, imagine a sphere described having its . . . This item ships from La Vergne,TN. Paperback. Nº de ref. de la librería 9781236266521

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Editorial:
Rarebooksclub.com, United States
(2012)

ISBN 10: 1236266528
ISBN 13: 9781236266521

Nuevos
Paperback
Cantidad: 10

Librería

Valoración

**Descripción **Rarebooksclub.com, United States, 2012. Paperback. Estado de conservación: New. 246 x 189 mm. Language: English . Brand New Book ***** Print on Demand *****. This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1898 Excerpt: .depend upon the radius, but yet so far as we have seen may depend upon the position of the spherical surface. This gives the mean value of ff over the sphere. Now let the sphere, without alteration of the radius, be displaced through a small distance dx in the direction of x. The change of the mean potential is 51 that is, dC/dx is the mean value of df/dx taken over the sphere. This vanishes when r is infinite since we suppose the fluid at rest at infinity. Hence dC/dx = 0 also when r is infinite. Similarly dC/dy = 0, dC/dz = 0. But C has the same value for all concentric spheres enclosing the inner bounding surfaces. Consider then two such spheres, one of finite radius, the other so large that df/dx is zero at every point of it, and let them be displaced together. Since dC/dx is zero for the large sphere it is also zero for the smaller. Thus C does not depend on the position of the centre of the sphere, and is the same for every spherical surface enclosing all the inner bounding surfaces. If the sphere considered be wholly situated in the region of irrotational motion the value of M is zero, and we have 52 that is, the average potential over the surface is independent of the radius of the sphere and is the same for all spheres having the same centre. The average potential over any sphere is therefore equal to that over an infinitesimal sphere surrounding the centre; that is, it is equal to the potential at the centre. This theorem is due to Gauss and, with the results which follow, is of great importance in the electrostatic analogue. 305. It follows that the potential cannot be constant over any finite portion S of the non-rotating fluid without being constant over the remainder. For, taking this not to be the case, imagine a sphere described having its . Nº de ref. de la librería APC9781236266521

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De Reino Unido a Estados Unidos de America

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Editorial:
Rarebooksclub.com, United States
(2012)

ISBN 10: 1236266528
ISBN 13: 9781236266521

Nuevos
Paperback
Cantidad: 10

Librería

Valoración

**Descripción **Rarebooksclub.com, United States, 2012. Paperback. Estado de conservación: New. 246 x 189 mm. Language: English . Brand New Book ***** Print on Demand *****.This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1898 Excerpt: .depend upon the radius, but yet so far as we have seen may depend upon the position of the spherical surface. This gives the mean value of ff over the sphere. Now let the sphere, without alteration of the radius, be displaced through a small distance dx in the direction of x. The change of the mean potential is 51 that is, dC/dx is the mean value of df/dx taken over the sphere. This vanishes when r is infinite since we suppose the fluid at rest at infinity. Hence dC/dx = 0 also when r is infinite. Similarly dC/dy = 0, dC/dz = 0. But C has the same value for all concentric spheres enclosing the inner bounding surfaces. Consider then two such spheres, one of finite radius, the other so large that df/dx is zero at every point of it, and let them be displaced together. Since dC/dx is zero for the large sphere it is also zero for the smaller. Thus C does not depend on the position of the centre of the sphere, and is the same for every spherical surface enclosing all the inner bounding surfaces. If the sphere considered be wholly situated in the region of irrotational motion the value of M is zero, and we have 52 that is, the average potential over the surface is independent of the radius of the sphere and is the same for all spheres having the same centre. The average potential over any sphere is therefore equal to that over an infinitesimal sphere surrounding the centre; that is, it is equal to the potential at the centre. This theorem is due to Gauss and, with the results which follow, is of great importance in the electrostatic analogue. 305. It follows that the potential cannot be constant over any finite portion S of the non-rotating fluid without being constant over the remainder. For, taking this not to be the case, imagine a sphere described having its . Nº de ref. de la librería APC9781236266521

Más información sobre esta librería | Hacer una pregunta a la librería

De Reino Unido a Estados Unidos de America

Destinos, gastos y plazos de envío