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formatted cross product and vectors.
Carl Brannen
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To understand what field is "real", write a charge equation of motion. The force in it is determined with the real field there. In a medium it is E: $m\vec{a} = q\vec{E}$. In case of magnetic field, it is $\vec{B}$ that determines the force: $m\vec{a} = q \vec{v} \times \vec{B}/c$.