Magnetic Fields: Difference between revisions
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Recall that according to Gauss' law, the electric flux through any closed surface is directly proportional to the net electric charge enclosed by that surface. Given the very direct analogy which exists between an electric charge and a magnetic 'monopoles', we would expect to be able to formulate a second law which states that the magnetic flux through any closed surface is directly proportional to the number of magnetic monopoles enclosed by that surface. But the problem is that magnetic monopoles don't exist. It follows that the equivalent of Gauss' law for magnetic fields reduces to: | Recall that according to Gauss' law, the electric flux through any closed surface is directly proportional to the net electric charge enclosed by that surface. Given the very direct analogy which exists between an electric charge and a magnetic 'monopoles', we would expect to be able to formulate a second law which states that the magnetic flux through any closed surface is directly proportional to the number of magnetic monopoles enclosed by that surface. But the problem is that magnetic monopoles don't exist. It follows that the equivalent of Gauss' law for magnetic fields reduces to: | ||
&Phi_B = \oint B \cdot dA = 0 | |||
Realistically, the magnetic flux though any closed surface is zero. This rule is useful when solving for a an unknown magnetic field that's coming from a side of a surface when the other fields from the other sides are known. | Realistically, the magnetic flux though any closed surface is zero. This rule is useful when solving for a an unknown magnetic field that's coming from a side of a surface when the other fields from the other sides are known. | ||
Revision as of 11:54, 25 November 2015
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The Main Idea
Recall that according to Gauss' law, the electric flux through any closed surface is directly proportional to the net electric charge enclosed by that surface. Given the very direct analogy which exists between an electric charge and a magnetic 'monopoles', we would expect to be able to formulate a second law which states that the magnetic flux through any closed surface is directly proportional to the number of magnetic monopoles enclosed by that surface. But the problem is that magnetic monopoles don't exist. It follows that the equivalent of Gauss' law for magnetic fields reduces to:
&Phi_B = \oint B \cdot dA = 0
Realistically, the magnetic flux though any closed surface is zero. This rule is useful when solving for a an unknown magnetic field that's coming from a side of a surface when the other fields from the other sides are known.