Magnetic scalar and vector potential

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Mathematically, Scalar V_m Magnetic Potential is given by

\overline{H}=∇V_m​

and Vector Magnetic Potential \overline{A} is given by

\overline{B}=\overline{∇}X\overline{A}​

Is there any way I can explain it or define it in words?
 
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The rotational (∇xA) and the irrotational (∇V) parts.
 
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