A description of the magnetic field strength, also considering its relation with the magnetic flux density
Key FactsGyroscopic Couple: The rate of change of angular momentum () = (In the limit).
- = Moment of Inertia.
- = Angular velocity
- = Angular velocity of precession.
Key facts The magnetic field strength is defined as:
For an isolated conductor of radius , the magnetic field strength is:
The magnetic field strength is related to the magnetic flux density by the equation:
where is the magnetic permeability of free space, and is the relative magnetic permeability of the material. <br/> Constants
The magnetic fields generated by electric currents are characterized by the magnetic flux density , measured in . But when the generated fields pass through magnetic materials which themselves contribute internal magnetic fields, ambiguities can arise concerning what part of the field comes from the external currents, and what part comes from the material itself. In order to clarify this issue, we introduce another magnetic field quantity, the magnetic fields strength , which unambiguously designates the magnetic influence from external currents, independent of the material's magnetic contribution. The magnetic field strength can be broadly defined by:
Magnetic Field Strength And Magnetic Flux DensityA commonly used relation between the magnetic flux density and the magnetic field strength is: 9) is the magnetic permeability of free space, also known as the magnetic constant:
Example - Magnetic flux of a toroid
Given a toroid with the mean diameter of and the cross section of (see Figure E1), calculate the number of ampere-turns () which would give a magnetic flux of . The curve for iron is given in Figure E2: Also, calculate the number of ampere-turns required to give the same magnetic flux in the hypothetical case that the toroid has an air gap of length (see Figure E3).
Given that the cross section of the toroid is (), the magnetic flux density in the iron should be: 1), and , we get the required ampere-turns for the air gap: 3) and (4), we obtain the total required ampere-turns for the toroid with an air gap:
For the toroid without an air gap, the required ampere-turns are:
For the toroid with an air gap, the total required ampere-turns are: