Amperes Circuital Law

What Is Ampere’s Law?

According to Ampere’s law, magnetic fields are related to the electric current produced in them. The law specifies the magnetic field that is associated with a given current or vice-versa, provided that the electric field doesn’t change with time. Ampere’s Law can be stated as:

Table. 1

	Electric Circuits	Magnetic Circuits
Cause	E	$\mathcal{F}$
Effect	I	$\Phi$
Opposition	R	$\mathcal{R}$

As mentioned in the introduction to this chapter, there is a broad similarity between the analyses of electric and magnetic circuits. This has already been demonstrated to some extent for the quantities in [Table 1]. If we apply the "cause" analogy to Kirchhoff's voltage law ( $ \sum V=0$), we obtain the following: Equation (1) is referred to as Ampere's circuital law. When it is applied to magnetic circuits, sources of mmf are expressed by the equation The equation for the mmf drop across a portion of a magnetic circuit can be found by applying the relationships where $\Phi$ is the flux passing through a section of the magnetic circuit and $R$ is the reluctance of that section. The reluctance, however, is seldom calculated in the analysis of magnetic circuits. A more practical equation for the mmf drop is where $H$ is the magnetizing force on a section of a magnetic circuit and $l$ is the length of the section. As an example of Eq. (1), consider the magnetic circuit appearing in [Fig. 1] constructed of three different ferromagnetic materials. Applying Ampere's circuital law, we have