## Inductance and Force Calculations in Electrical CircuitsThis book deals with the two fundamental subjects of electromagnetism. It is a useful text for courses in electromagnetism, electrical circuits, mathematical methods of physics, and the history and philosophy of science. It covers how to calculate force between two current carrying circuits, and net force on a part of a closed circuit. The calculation of the mutual inductance between two circuits and self-inductance of a single closed circuit is also described. Experiments explain the main expressions of Ampere and Grassmann. A must to help deepen the knowledge of the mind of any student of science. |

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### Contents

Inductance Coefficients | 3 |

12 Current Element | 4 |

13 Neumanns Inductance | 6 |

14 Webers Inductance | 8 |

142 Webers Energy Between Current Elements | 9 |

143 Webers Expression | 10 |

15 Maxwells Inductance | 11 |

152 Maxwells Energy Between Current Elements | 12 |

52 Grassmanns Force | 55 |

522 Grassmanns Force Between Current Elements | 57 |

53 Partial Equivalence | 59 |

54 Description of the Method | 63 |

Force in Several Geometries | 65 |

612 Orthogonal Wires | 67 |

613 Rectangular Circuit | 68 |

62 Surface Element | 73 |

16 Graneaus Inductance | 14 |

17 Equivalence of the Mutual Inductances | 15 |

SelfInductance | 17 |

22 Method for Calculating Inductances | 18 |

23 Comparison with Known Results | 20 |

232 Cylinder with Axial Current | 23 |

233 Coaxial Cable | 24 |

Inductance in Several Geometries | 29 |

312 Straight and Orthogonal Conductors | 30 |

32 Surface Element | 32 |

322 Rectangular Surfaces in Contact | 33 |

323 Rectangular Circuit | 34 |

33 Volumetric Element | 36 |

332 Rectangular Circuit | 39 |

Complete Equivalence | 41 |

42 Proof of Equivalence | 44 |

Force Between Current Elements | 51 |

511 Webers Force | 52 |

622 Rectangular Circuit II | 77 |

623 Rectangular Circuit III | 79 |

Grassmanns Force | 81 |

63 Volumetric Element | 84 |

632 Discussion | 88 |

64 Solenoid with Poloidal Current | 90 |

Complete Equivalence | 93 |

72 Proofs of Equivalence | 96 |

Final Discussion | 103 |

82 Relation Between Inductance and Force | 105 |

83 Longitudinal force | 107 |

Conclusions | 117 |

Approximation Method for Integrals | 119 |

Example of the Method | 123 |

125 | |

135 | |

### Common terms and phrases

according to Grassmann's action and reaction Ampere and Grassmann's Ampere's expression Ampere's force approximation method arbitrary form bootstrap effect bridge due calculate the force calculate the self-inductance capacitor Chapter circuit of arbitrary circuit of Fig closed circuit Cj coaxial cable consider cross-section current flow Darwin's lagrangian discuss displacement current electrical electromagnetism energy between current equivalence between Ampere exact differential exact result experimental experiments fact Figure finite force acting force between current force exerted formulas of Neumann geometry given by Eq Grassmann's expressions Grassmann's force integration yields interaction energy limits of integration linear current elements longitudinal force Lorentz's force Maxwell and Graneau Maxwell's Moyssides mutual inductance net force obtained open circuit orthogonal poloidal current potential energy railgun Rectangular Circuit represented in Fig second order Section solenoid Solving these integrals Substituting surface or volumetric tension torsion balance valid volumetric current elements Weber's electrodynamics Weber's force whole circuit zero

### Popular passages

Page x - , 2 dr 527.] Of these four different assumptions that of Ampere is undoubtedly the best, since it is the only one which makes the forces on the two elements not only equal and opposite but in the straight line which joins them.

Page 132 - W. Weber. On the measurement of electro-dynamic forces. In R. Taylor, editor, Scientific Memoirs, vol. 5, pages 489-529, New York, 1966. Johnson Reprint Corporation.

Page 132 - JP Wesley. Weber electrodynamics, Part I. General theory, steady current effects. Foundations of Physics Letters, 3:443-469, 1990.

Page vii - To the Institutes of Physics and Mathematics of the State University of Campinas - UNICAMP which gave us the necessary conditions to undertake this work.

Page 132 - JP Wesley. Selected Topics in Advanced Fundamental Physics. Benjamin Wesley Publisher, Blumberg, 1991.