## The Mathematical Theory of Electricity and Magnetism |

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axis battery becomes body boundary centre circuit closed surface coefficients coil components condenser conductor constant coordinates Coulomb's Law current flowing cylinder denote dielectric differential direction disc distance distribution dxdydz earth electric force electric intensity electrification electromagnetic electromotive force electrons electrostatic units energy equal equilibrium equipotential expression field of force function galvanometer given Green's Theorem harmonics Hence induced charge inductive capacity infinite infinity inside insulated inverse J. J. THOMSON Laplace's equation Let us suppose lines of force magnetic field magnetic force magnetic particle magnetic potential magnetisation mechanical force medium molecules motion negative normal number of tubes obtain Ohm's Law parallel plane plate point charge polarisation pole positive potential produced quantity regarded resistance result Riemann's surface right angles shell Shew solution spherical spherical harmonic strength surface density surface integral theorem theory total charge transformation tubes of force uncharged unit area vanishes velocity wire zero

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Page 126 - Induction appears to consist in a certain polarized state of the particles, into which they are thrown by the electrified body sustaining the action, the particles assuming positive and negative points or parts, which are symmetrically arranged with respect to each other and the inducting surfaces or particles*.

Page 411 - ... and the ratio of the volume of the nucleus to that of the shell is properly chosen. Prove also that the field inside the nucleus is uniform, and that its intensity is greater or less than that outside according as p is greater or less than / 1 , . 8.

Page 220 - Q — 7T, and which has only a finite number of discontinuities and of maxima and minima...

Page 22 - II. When one body electrifies another by conduction, the total electrification of the two bodies remains the same, that is, the one loses as much positive or gains as much negative electrification as the other gains of positive or loses of negative electrification. For if the two bodies are enclosed in the hollow vessel, no change of the total electrification is observed.

Page 460 - A condenser of capacity C is connected by leads of resistance r, so as to be in parallel with a coil of self-induction L, the resistance of the coil and its leads being R. If this arrangement forms part of a circuit in which there is an electromotive force of...

Page 437 - A long straight current intersects at right angles a diameter of a circular current, and the plane of the circle makes an acute angle a with the plane through this diameter and the straight current.

Page 438 - A current i flows in a rectangular circuit whose sides are of lengths 2a, 26, and the circuit is free to rotate about an axis through its centre parallel to the sides of length 2a. Another current i' flows in a long straight wire parallel to the axis and at a distance d from it.

Page 137 - Qo(p'))la> where m is the total strength and // = cos 6', where & is the polar angle at the end a. 3. The motion of fluid is given by the velocity potential in which C is constant, and r and 6 are spherical polar coordinates. Determine the stream function. (UL) 4. A sphere of radius a is surrounded by a concentric spherical shell of radius 6, and the space between is filled with liquid. If the sphere be moving with velocity F, show that and find the current function.

Page 458 - A coil is rotated with constant angular velocity o, about an axis in its plane in a uniform field of force perpendicular to the axis of rotation. Find the current in the coil at any time, and shew that it is greatest when the plane of the coil makes an angle with the lines of magnetic force.