The Calculation Of Inductance For Air-cored Solenoid Coil

Air-cored solenoid coil is applied widely to the regions such as electron, electrical engineering and radio technique. The value on inductance of air-cored solenoid coil depends on the dimension and the shape of the coil, which is a parameter illuminating the attribute of the coil. There is a closely relationship between the inductance and some problems such as magnetic energy and interaction between coils. So how to calculate rapidly, expediently and precisely the inductance of the coil is an important problem. Based on the electromagnetic theories, this dissertation presents analytical method to solve the magnetic field caused by the air-cored solenoid coil. Using the vector potential, the expression for calculating self-inductance of the coil is derived. Below is the compendium of the dissertation:1. By giving a series of rational suppositions, the solving model of air-cored solenoid coil is built.2. The boundary value problem on the magnetic vector potential A is derived by introducing the magnetic vector potential A and using Maxwell's equations. Through solving the boundary value problem, the magnetic vector potential A is gained. And the expression of magnetic flux density B is got by making use of the relation of magnetic vector potential A and magnetic flux density B. Finally, the equation of the magnetic flux lines is given by way of describing the distributing of the magnetic field.3. Using the vector potential, the expression for calculating inductanceof air-cored solenoid coil is derived in the dissertation. And the calculatingmethods of function T in the calculating expression are given for the convenience of the calculation of inductance while the precision is not strictly requested. At last, the expression on the mutual inductance of the coaxial air-cored solenoid coil is given.4. The inductance expression obtained in the dissertation can offer theoretical guidance to the design of the air-cored solenoid coil. Using the given inductance expression and calculating tables can rapidly and expediently calculate the inductance of the coil. And the gained result has higher precision, which completely satisfies the requirement of the general engineering application.