5.3 M AGNETISM AND G AUSS ’ S L AW

. M AGNETISM AND G AUSS ’ S L AW In Chapter , we studied Gauss’s law for electrostatics. In Fig . (c), we see that for a closed surface represented by i , the number of lines leaving the surface is equal to the number of lines entering it. This is consistent with the fact that no net charge is enclosed by the surface. However, in the same figure, for the closed surface ii , there is a net outward flux, since it does include a net (positive) charge. E XAMPLE . The situation is radically different for magnetic fields which are continuous and form closed loops. Examine the Gaussian surfaces represented by i or ii in Fig . (a) or Fig. . (b). Both cases visually demonstrate that the number of magnetic field lines leaving the surface is balanced by the number of lines entering it. The net magnetic flux is zero for both the surfaces . This is true for any closed surface. FIGURE . Consider a small vector area element ∆ S of a closed surface S as in Fig. . . The magnetic flux through ÄS is defined as ∆φ B = B . ∆ S , where B is the field at ∆ S . We divide S into many small area elements and calculate the individual flux through each. Then, the net flux φ B is, ' ' ' ' B B all all φ φ ∆ ∆