Ampere’s Law

First discovered by André-Marie Ampère in 1826
Definition: The integral around a closed path of the component of the magnetic field tangent to the direction of the path equals µ0 times the current intercepted by the area within the path
1. Or, in a simplified scalar form:
  1. Thus the line integral (circulation) of the magnetic field around some arbitrary closed curve is proportional to the total current enclosed by that curve
2. exercise: If we know that an electric current of 12 A flows through an empty 5 cm solenoid and the magnetic field created inside it is 0.1 T. How many turns is the solenoid made up of?
  1. To determine the number of turns, it suffices to apply the formula of the magnetic field generated inside a solenoid and replace the values that we know:
Bibliography: https://web.iit.edu/sites/web/files/departments/academic-affairs/academic-resource-center/pdfs/Amperes_law.pdf - http://hyperphysics.phy-astr.gsu.edu/hbasees/magnetic/amplaw.html#c2
In order to apply Ampère’s Law all currents have to be steady (i.e. do not change with time)
Only currents crossing the area inside the path are taken into account and have some contribution to the magnetic field
Currents have to be taken with their algebraic signs (those going “out” of the surface are positive, those going “in” are negative)- use right hand’s rule to determine directions and signs
The total magnetic circulation is zero only in the following cases: -the enclosed net current is zero -the magnetic field is normal to the selected path at any point -the magnetic field is zero
Ampère’s Law can be useful when calculating magnetic fields of current distributions with a high degree of symmetry (similar to symmetrical charge distributions in the case of Gauss’ Law)
Applications of the Ampere Law
1. Magnetic Field of a Solenóide
2. Magnetic Field of a Toróide
  1. The toróide is a very useful device that is used in many areas, from tape heads to tokamaks.
3. Magnetic Field by Current
4. Magnetic Force Between Cables

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Ampere’s Law

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