|MadSci Network: Physics|
I could not find the exact equation you cite in your question, although there are similar equations for solenoids, for example. The magnetic field strength, H, is actually equal to (B - ľo M) / ľo , where B is the magnetic field, M is the magnetization (magnetic moment per unit volume of a core, like a core of iron inside a solenoid that can get magnetized), and ľo is the permeability constant, 1.26E-6 henry/meter. In any case, these sort of equations regarding magnetic field strength are based on the Biot-Savart law: H=Integral[(Idl X a)/(4*PI*R^2)]. (A/m) The Biot-Savart Law is like Coulomb's law, but for magnetostatics. It was derived from experimental observations. Similarly, the linear relationship between magnetic field strenghth and current was also apparently based on experimental observation. With zero current, there was no (zero) magnetic field strenghth. As the current was increased, the magnetic field strength increased linearly. Some useful references that might help to further understand this would be: 1) Halliday and Resnick, Physics (Parts I and II), chapters 34, 35, and 37, especially pages 936-940. 2) Skitek and Marshall, Electromagnetic Concepts and Applications, chapter 8, pages 222-254.
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