Gauss's law for magnetic fields
1. Magnetic flux
We introduce the magnetic flux for a magnetic field crossing
a surface as we did for an electric field. If we divide a surface S
into infinitesimal area elements dS. At a point on the surface S,
the direction of an area element is perpendicular to the surface.
the magnetic flus is written as:
→ →
dΦB = B . dS
Over the whole surface S, we integrate to obtain the magnetic flux
ΦB of the magnetic field B through the surface S:
→ →
ΦB = ∫ B . dS
2. Gauss's law for magnetic fields
A line representing the electric field does not close on itself. It
has a beginning at (+q). In the case of a electric dipole, the line ends at (-q).
Gauss's law for the electric field gives the magnitude of the
flux of an electric field E intersecting a closed surface S:
→ →
ΦE = ∮ E . dS = Σq/εo
Σdq is the algebraic sum of the charge within the volume
enclosed by the surface.
For any closed surface in a magnetic field, each
line of the magnetic field that pierces into the closed surface at
one point also pierces out of this closed surface at some other point.
The net number of lines that cross the closed surface is zero.
The magnetic charge does not exist in nature, and there is no a
magnetic monopole; that is we cannot isolate a magnetic pole.
The simplest source of an electric field is a point charge, whereas
the simplest source of a magnetic field is a magnetic dipole.
A line representing the magnetic field always closes on itself
having no beginning and no end.
→ →
ΦB = ∮B.dS = 0
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