If Div B = 0, where B = magnetic field intensity, then B must be a Curl of a some vector function. What is that vector function?

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Abigailf91er · Accepted Answer

It is called the electromagnetic vector potential, A(r,t)      B    (      r    ,  t  )  =  ∇  ×      A    (      r    ,  t  )where the operator,   ∇  ×, is the curl. The electric field has also a part derived from it, as follows:      E    (      r    ,  t  )  =  −  ∇  ϕ  (      r    ,  t  )  −            ∂              A            (              r            ,      t      )              ∂      t      where   ϕ  (      r    ,  t  ) is the scalar potential.These two definitions arise from the Maxwell equations, however,       A   and   ϕ are not unique, they can always be shifted by a continuous function,   χ  (      r    ,  t  ), such that, transforming      A    (      r    ,  t  )  →      A    (      r    ,  t  )  +  ∇  χ  (      r    ,  t  )    ϕ  (      r    ,  t  )  →  ϕ  (      r    ,  t  )  −            ∂      χ      (              r            ,      t      )              ∂      t      will also satisfy the Maxwell equations. This is called gauge transformation.

If Div B = 0, where B = magnetic field

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