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hetriamhageh6k20

hetriamhageh6k20

Answered question

2022-05-17

Gauss's Law for magnetism is
B = 0
This allows us to write the magentic field B as the curl of another field the magnetic vector potential, A.
B = × A
This adhers to ( × A ) = 0
However, if a monopole does exist then we have
B = ρ m
Where ρ m is some magnetic charge density however with a magentic vector potential this violates the equation, ( × A ) 0
Does that mean if magnetic monopoles does exist, that the magnetic field can no longer be defined by a magnetic vector potential? In which case how was dirac able to still define the magnetic field by a magnetic vector potentials?

Answer & Explanation

Lea Johnson

Lea Johnson

Beginner2022-05-18Added 13 answers

That means that, in general, you will have to write B = ψ + × A . Then B = 2 ψ = ρ m . Of course ( × A ) = 0 for any vector field A, as d 2 = 0

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