In chapter 1, we studied Gauss's law for electrostatics. For a closed surface 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 one, for the closer surface, there is a net outward flux, since it does include a net (positive) charge.
The situation is radically different for magnetic fields which are continuous and form closed loops. Both cases visually demonstrate that the number of lines of force 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.
Consider a small vector area element delta S of a closed surface S. The magnetic flux through delta S is defined as delta phi B = B.x delta S. where B is the field at delta S. We divide S into many small area elements and calculate the individual flux through each. Then the net flux phi B is,
phi B= sigma phi B= sigma B.delta S=0
where all stands for all area elements delta S.
Thus Gauss law for magnetism is:
The net magnetic flux through any closed surface is zero. The difference between the Gauss's law of magnetism and that for electrostatics is a reflection of the fact that isolated magnetic poles (also called monopoles) are not known to exist.
The situation is radically different for magnetic fields which are continuous and form closed loops. Both cases visually demonstrate that the number of lines of force 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.
Consider a small vector area element delta S of a closed surface S. The magnetic flux through delta S is defined as delta phi B = B.x delta S. where B is the field at delta S. We divide S into many small area elements and calculate the individual flux through each. Then the net flux phi B is,
phi B= sigma phi B= sigma B.delta S=0
where all stands for all area elements delta S.
Thus Gauss law for magnetism is:
The net magnetic flux through any closed surface is zero. The difference between the Gauss's law of magnetism and that for electrostatics is a reflection of the fact that isolated magnetic poles (also called monopoles) are not known to exist.
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