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- https://phys.libretexts.org/Bookshelves/Electricity_and_Magnetism/Electromagnetics_I_(Ellingson)/07%3A_Magnetostatics/7.04%3A_Amperes_Circuital_Law_(Magnetostatics)_-_Integral_FormThe integral form of Amperes’ Circuital Law (ACL) for magnetostatics relates the magnetic field along a closed path to the total current flowing through any surface bounded by that path.
- https://phys.libretexts.org/Courses/Kettering_University/Electricity_and_Magnetism_with_Applications_to_Amateur_Radio_and_Wireless_Technology/20%3A_Maxwell's_Equations/20.04%3A_Amperes_LawA fundamental property of a static magnetic field is that, unlike an electrostatic field, it is not conservative. A conservative field is one that does the same amount of work on a particle moving bet...A fundamental property of a static magnetic field is that, unlike an electrostatic field, it is not conservative. A conservative field is one that does the same amount of work on a particle moving between two different points regardless of the path chosen. Magnetic fields do not have such a property. Instead, there is a relationship between the magnetic field and its source, electric current. It is expressed in terms of the line integral B and is known as Ampère’s law.
- https://phys.libretexts.org/Courses/Kettering_University/Electricity_and_Magnetism_with_Applications_to_Amateur_Radio_and_Wireless_Technology/18%3A_Calculation_of_Magnetic_Quantities_from_Currents/18.05%3A_Magnetic_Field_of_Solenoids_and_ToroidsTwo of the most common and useful electromagnetic devices are called solenoids and toroids. In one form or another, they are part of numerous instruments, both large and small. In this section, we exa...Two of the most common and useful electromagnetic devices are called solenoids and toroids. In one form or another, they are part of numerous instruments, both large and small. In this section, we examine the magnetic field typical of these devices.
- https://phys.libretexts.org/Courses/Berea_College/Electromagnetics_I/07%3A_Magnetostatics/7.04%3A_Amperes_Circuital_Law_(Magnetostatics)_-_Integral_FormThe integral form of Amperes’ Circuital Law (ACL) for magnetostatics relates the magnetic field along a closed path to the total current flowing through any surface bounded by that path.
- https://phys.libretexts.org/Courses/Berea_College/Electromagnetics_I/07%3A_Magnetostatics/7.09%3A_Amperes_Law_(Magnetostatics)_-_Differential_FormIn this section, we derive the differential form of Amperes’ Circuital Law. In some applications, this differential equation, combined with boundary conditions associated with discontinuities in struc...In this section, we derive the differential form of Amperes’ Circuital Law. In some applications, this differential equation, combined with boundary conditions associated with discontinuities in structure and materials, can be used to solve for the magnetic field in arbitrarily complicated scenarios. A more direct reason for seeking out this differential equation is that we gain a little more insight into the relationship between current and the magnetic field.
- https://phys.libretexts.org/Bookshelves/University_Physics/Calculus-Based_Physics_(Schnick)/Volume_B%3A_Electricity_Magnetism_and_Optics/B35%3A_Gausss_Law_for_the_Magnetic_Field_and_Amperes_Law_RevisitedRemember Gauss’s Law for the electric field? It’s the one that, in conceptual terms, states that the number of electric field lines poking outward through a closed surface is proportional to the amoun...Remember Gauss’s Law for the electric field? It’s the one that, in conceptual terms, states that the number of electric field lines poking outward through a closed surface is proportional to the amount of electric charge inside the closed surface.
- https://phys.libretexts.org/Courses/Berea_College/Introductory_Physics%3A_Berea_College/22%3A_Source_of_Magnetic_Field/22.03%3A_Amperes_LawAmpere’s Law is similar to Gauss’ Law, as it allows us to (analytically) determine the magnetic field that is produced by an electric current in configurations that have a high degree of symmetry
- https://phys.libretexts.org/Courses/Muhlenberg_College/Physics_122%3A_General_Physics_II_(Collett)/08%3A_Sources_of_Magnetic_Fields/8.06%3A_Amperes_LawA fundamental property of a static magnetic field is that, unlike an electrostatic field, it is not conservative. A conservative field is one that does the same amount of work on a particle moving bet...A fundamental property of a static magnetic field is that, unlike an electrostatic field, it is not conservative. A conservative field is one that does the same amount of work on a particle moving between two different points regardless of the path chosen. Magnetic fields do not have such a property. Instead, there is a relationship between the magnetic field and its source, electric current. It is expressed in terms of the line integral B and is known as Ampère’s law.
- https://phys.libretexts.org/Courses/Berea_College/Electromagnetics_I/08%3A_Time-Varying_Fields/8.09%3A_Displacement_Current_and_Amperes_LawIn this section, we generalize Ampere’s Law, previously encountered as a principle of magnetostatics. We shall now demonstrate that this equation is unreliable if the current is not steady; i.e., not ...In this section, we generalize Ampere’s Law, previously encountered as a principle of magnetostatics. We shall now demonstrate that this equation is unreliable if the current is not steady; i.e., not DC.
- https://phys.libretexts.org/Bookshelves/Electricity_and_Magnetism/Electromagnetics_I_(Ellingson)/04%3A_Vector_Analysis/4.08%3A_CurlCurl is an operation, which when applied to a vector field, quantifies the circulation of that field. The concept of circulation has several applications in electromagnetics.
- https://phys.libretexts.org/Courses/Georgia_State_University/GSU-TM-Physics_II_(2212)/06%3A_Sources_of_Magnetism_Magnetic_Forces_and_Fields/6.07%3A_Solenoids_and_ToroidsThe magnetic field inside a toroid is not uniform, as it varies inversely with the distance r from the axis OO’. However, if the central radius R (the radius midway between the inner and outer radii o...The magnetic field inside a toroid is not uniform, as it varies inversely with the distance r from the axis OO’. However, if the central radius R (the radius midway between the inner and outer radii of the toroid) is much larger than the cross-sectional diameter of the coils r, the variation is fairly small, and the magnitude of the magnetic field may be calculated by Equation ??? where r=R.