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As you know, in CGS units we have vacuum permeability as unity (1). so H=B and we use Oersted for H.

on the other hand, in SI, permeability is (4 x pi x 0.0000001) and we use Ampere per meter for H. unfortunately after trying for couple hours, I couldn't derive the algebra of converting these to each other. everywhere they simply say just multiply 1000/(4 x pi) to amper per meter. but why? and how to derive this conversion coefficient?

I know that cgs is cm gram second and si is meter kilogram second and i know how to convert these, but when amperes come into play and when the formulas are different in a coefficient, I just get confused.

I apologies in advance if this looks ridiculous.