Electricity and Magnetism: An Introduction to the by Arthur Stanley Ramsey

By Arthur Stanley Ramsey

A. S. Ramsey (1867-1954) used to be a distinctive Cambridge mathematician and President of Magdalene collage. He wrote numerous textbooks 'for using better divisions in colleges and for first-year scholars at university'. This booklet on electrical energy and magnetism, first released in 1937, and dependent upon his lectures over a long time, used to be 'adapted extra rather to the desires of applicants for half I of the Mathematical Tripos'. It covers electrostatics, conductors and condensers, dielectrics, electric pictures, currents, magnetism and electromagnetism, and magnetic induction. The booklet is interspersed with examples for resolution, for a few of which solutions are supplied.

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Prove that the extreme lines of force which pass from A to iSmake, on leaving A, an angle 9 with AB, where cos0 = (e—2e')/e; and indicate by a figure the general form of the lines of force. [M. T. 1907] 20. Draw a rough diagram to show the distribution of lines of force and equipotential surfaces due to two point charges, one of them being 4e and the other - 3e. [I. 1909] 21. Charges + 1 , — 4, + 1 are placed at coUinear points A, B and O, where AB = B0. Sketch the lines of force; and shew that any line of force leaving C will reach B at an inclination to BO less than \n.

We must comment on the fact that equation (2) contains a volume density p of electricity; and we have stated that charges reside upon surfaces and we should therefore expect that they would enter into calculations as surface density or charge per unit area. But a charge per unit area is really a charge occupying a volume though concentrated by the fact that one dimension of the volume is indefinitely diminished, and it is often convenient in theoretical work to assume the existence of volume densities and treat surface densities as limiting cases.

AT* Let an element PP' of a line of force subtend angles dd1, dd2, dd3, ... , then since the total flux of intensity across PP' is zero, therefore 2exddx + 2e2d62 + 2e3d63 +... = 0, or, by integration, ex 01 + e202 + e303 + ... = const (1), where the d's are the angles made by the lines AXP, A2P, A3P, ... with any fixed direction. For different values of the constant, equation (1) represents the lines of force in any cross-section of the field. It should be noticed that if any point A lies on the opposite side of the line of force to the other points the sign of the corresponding term in the equation must be changed.

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