14Static and Quasi‐Static Magnetic Fields

In the study of static electric fields, we learned that static distributions of charge led to the definition of the two fundamental vectors:

  • electric field intensity E
  • electric flux density D

In the study of static magnetic fields, we will learn that a steady movement of charge (dc current) leads to the definition of the remaining two fundamental vectors:

  • magnetic field intensity H
  • magnetic flux density B

Static electric and static magnetic fields, and their corresponding vectors, can be studied independently. In the time‐varying case, the fields are no longer independent (hence the name electromagnetic), and all four vectors are involved in the field description.

14.1 Magnetic Flux Density

Recall that the electric field intensity E at a point in space has been defined in terms of the electric force Fe acting on a test charge when placed at that point:

We could refer to Eq. (14.1) as an explicit definition of the electric field intensity. Equivalently, Eq. (14.1) could be written as

(14.2)images

and we could refer to it as an implicit definition of the electric field intensity.

In a similar manner, we define the magnetic flux density B at a point in space in terms of the magnetic force Fm that would be exerted on a charged particle passing with a velocity ...

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