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CHAPTER 7   The Steady Magnetic Field         207

                     7.5 MAGNETIC FLUX AND MAGNETIC
                            FLUX DENSITY
                     In free space, let us define the magnetic flux density B as

                                           B = µ 0 H  (free space only)              (32)

                                                                 2
                     where B is measured in webers per square meter (Wb/m )orinanewer unit adopted
                     in the International System of Units, tesla (T). An older unit that is often used for
                                                                    2
                     magnetic flux density is the gauss (G), where 1 T or 1Wb/m is the same as 10, 000 G.
                     The constant µ 0 is not dimensionless and has the defined value for free space, in henrys
                     per meter (H/m), of

                                              µ 0 = 4π × 10 −7  H/m                  (33)

                     The name given to µ 0 is the permeability of free space.
                         We should note that since H is measured in amperes per meter, the weber is
                     dimensionally equal to the product of henrys and amperes. Considering the henry as
                     anew unit, the weber is merely a convenient abbreviation for the product of henrys
                     and amperes. When time-varying fields are introduced, it will be shown that a weber
                     is also equivalent to the product of volts and seconds.
                         The magnetic-flux-density vector B,as the name weber per square meter im-
                     plies, is a member of the flux-density family of vector fields. One of the possible
                                                          7
                     analogies between electric and magnetic fields compares the laws of Biot-Savart and
                     Coulomb, thus establishing an analogy between H and E. The relations B = µ 0 H
                     and D =   0 E then lead to an analogy between B and D.If B is measured in teslas or
                     webers per square meter, then magnetic flux should be measured in webers. Let us
                     represent magnetic flux by 
 and define 
 as the flux passing through any designated
                     area,


                                               
 =    B · dS Wb                      (34)
                                                    S
                         Our analogy should now remind us of the electric flux  , measured in coulombs,
                     and of Gauss’s law, which states that the total flux passing through any closed surface
                     is equal to the charge enclosed,


                                                 =   D · dS = Q
                                                    S
                     The charge Q is the source of the lines of electric flux and these lines begin and
                     terminate on positive and negative charges, respectively.





                     7  An alternate analogy is presented in Section 9.2.
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