Why is it advantageous to use vectors D and A in problems?

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Sammy268
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At the moment we are working through problems in Griffiths' Electrodynamics textbook and it got me thinking...

In magnetostatics we have the magnetic vector potential A and in the use of dielectrics problems we have the vector D. Why is it advantageous to use these vectors and not just stick to using B and E?
 
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