On a basic level why can't monopoles exist?

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SUMMARY

Magnetic monopoles cannot exist due to the fundamental nature of magnetic fields as described by Maxwell's equations, specifically the equation ∇·B = 0, which indicates that magnetic field lines are continuous and do not begin or end. A moving positive electric charge generates a magnetic field with two poles, resulting in closed-loop field lines rather than isolated monopoles. This discussion clarifies that the presence of two poles is inherent to the structure of magnetic fields created by electric charges.

PREREQUISITES
  • Understanding of Maxwell's equations, particularly ∇·B = 0
  • Basic knowledge of electromagnetic theory
  • Familiarity with the concept of electric charge and magnetic fields
  • Concept of field lines in physics
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  • Research the concept of magnetic field lines and their properties
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Physics students, educators, and anyone interested in understanding the fundamental principles of electromagnetism and the nature of magnetic fields.

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Homework Statement



If a positive electric charge can create a magnetic field (because all you need to create a magnetic field is a moving charge), how is there 2 poles in this magnetic field created by this positive electric charge. Why isn't the magnetic field created by a single positive electric charge considered a monopole?
 
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Are we mixing up things ? In your description, where exactly do you locate the 2 poles you mention ?
 
Other approach: if there were magnetic monopoles, there would be magnetic field lines coming out of e.g. a sphere surrounding such a thingy -- without magnetic field lines going in. But the magnetic field lines from a moving charge are neat circles, all of them. No beginning, no end.

The sophisticated way to express this is ##\nabla\cdot{\bf \vec B}=0##, one of the Maxwell equations
 

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