Gauss' Law for Magnetism and Electricity
Why is magnetic flux through closed surface zero while electric flux not?
Gauss' Law for Magnetism
The net magnetic flux out of any closed surface is zero. This amounts to a statement about the sources of magnetic field. For a magnetic dipole, any closed surface the magnetic flux directed inward toward the south pole will equal the flux outward from the north pole. The net flux will always be zero for dipole sources. If there were a magnetic monopole source, this would give a non-zero area integral. The divergence of a vector field is proportional to the point source density, so the form of Gauss' law for magnetic fields is then a statement that there are no magnetic monopoles.
Gauss' Law for Electricity
The electric flux out of any closed surface is proportional to the total charge enclosed within the surface.
The integral form of Gauss' Law finds application in calculating electric fields around charged objects.
In applying Gauss' law to the electric field of a point charge, one can show that it is consistent with Coulomb's law.
While the area integral of the electric field gives a measure of the net charge enclosed, the divergence of the electric field gives a measure of the density of sources. It also has implications for the conservation of charge.
Consider flux as being the total of the field lines that enter and leave through a closed surface. Magnetic field lines are loops (for a simple bar magnet, from N to S and, inside the magnet, back to N); every loop that exits a closed surface must also leave it. Electical field lines do not loop. They originate at positive poles and radiate outward, or they converge and terminate at negative poles, or both. All of the electrical field lines from any charge included in the closed surface must either leave (positive charge) or enter (negative charge), but not both.
Because there are no magnetic monopoles, whereas electric monopoles (charged objects) are everywhere. No particle has been discovered
Gauss' Law for Magnetism
The net magnetic flux out of any closed surface is zero. This amounts to a statement about the sources of magnetic field. For a magnetic dipole, any closed surface the magnetic flux directed inward toward the south pole will equal the flux outward from the north pole. The net flux will always be zero for dipole sources. If there were a magnetic monopole source, this would give a non-zero area integral. The divergence of a vector field is proportional to the point source density, so the form of Gauss' law for magnetic fields is then a statement that there are no magnetic monopoles.
Gauss' Law for Electricity
The electric flux out of any closed surface is proportional to the total charge enclosed within the surface.
The integral form of Gauss' Law finds application in calculating electric fields around charged objects.
In applying Gauss' law to the electric field of a point charge, one can show that it is consistent with Coulomb's law.
While the area integral of the electric field gives a measure of the net charge enclosed, the divergence of the electric field gives a measure of the density of sources. It also has implications for the conservation of charge.
Consider flux as being the total of the field lines that enter and leave through a closed surface. Magnetic field lines are loops (for a simple bar magnet, from N to S and, inside the magnet, back to N); every loop that exits a closed surface must also leave it. Electical field lines do not loop. They originate at positive poles and radiate outward, or they converge and terminate at negative poles, or both. All of the electrical field lines from any charge included in the closed surface must either leave (positive charge) or enter (negative charge), but not both.
Because there are no magnetic monopoles, whereas electric monopoles (charged objects) are everywhere. No particle has been discovered