... Gauss\' Law for magnetic fields Unlike electric fields that may be produced
ID: 2842601 • Letter: #
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Gauss' Law for magnetic fields Unlike electric fields that may be produced by a single point charge, magnetic fields cannot originate from a single pole. For example, ordinary bar magnets have two poles, a north and a south pole. Figure 1 illustrates the magnetic field, denoted by the vector field B, around a bar magnet. By drawing various closed surfaces in the vector field, explain why the flux of the magnetic field across any closed surface is zero. The second of Maxwell's laws states that for any magnetic field (not just bar magnets) the flux of the magnetic field across any closed surface is zero; that is. Use the Divergence Theorem to derive the differential form at the law, Explain why magnetic monopoles (single point sources of magnetic fields) violate this law; thus monopoles cannot exist.Explanation / Answer
a. 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.
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