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Understanding Ampere’s Circuital Law: Applications in Magnetic Fields and Conductors

This chapter delves into Ampere’s Circuital Law and its application in various magnetic field scenarios. We explore the behavior of long cylindrical conductors, where the total current through a surface is calculated as I × N. The chapter illustrates concepts with examples such as the toroidal coil and the refraction of magnetic field lines at a current sheet. Additionally, we examine the properties of short solenoids, emphasizing the negligible end effects in long solenoids while utilizing cylindrical coordinates for analysis.

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Understanding Ampere’s Circuital Law: Applications in Magnetic Fields and Conductors

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  1. Chapter 9 Magnetic Fields:II • Ampere’s Circuital Law • Example:Long Cylindrical Conductor • Example:Toroidal Coil • Example:Refraction of Lines of B at a Current Sheet • Short Solenoid • The Curl of B

  2. In many cases the same current crosses the surface bounded by the curve C several times. See Fig. 9-2(b) for a solenoid. Then the total current is I×N.

  3. Example: Long Solonoid (see Figs. 9-6 and 9-7） It is very long so that the end effects will negligible. Choose a cylindrical coordinates.

  4. Example: Refraction of Lines of B at a Current Sheet A thin conducting sheet carries a current density α(ampere / meter). (See Fig.9-8)

  5. Example: Short Solonoid See Fig. 9-9 The solonoid has a length l and radius a.

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