Magnetic field produced by a moving charge

[louf]

Assuming constant velocity of an electric charge produces a magnetic field, electrons in orbit have a magnetic field. The uniform alignment will collaborate to make a strong field (a magnet or magnetized iron), otherwise their random motion will have cancelling effects of the magnetic fields and no appreciable field will be noticed (although the magnetic fields are there). Is this true?

[louf]

Is this correct: a charge produces an electric field; a moving charge (constant velocity) produces a magnetic field? I am asking because I was under the impression that changing velocity (acceleration or deaccelaration) is what produces the magnetic field e.g. no magnetic field in DC, but it exists in AC.

[adosar]

yes but magnetic fields travel at speed of light at vacuum. So when the partical has distance r from the point we try to find the magnetic field the magnetic field shouldn't reach the point .

[louf]

A bit off-topic, I know the enigmatic fundamental of everything is known as "energy", but it seems all of everything exists because of electric charge.

[jacobvandijk]

CORRECTION: In your equation including the crossproduct of v and r the denominator should be r^3 ! The result of the crossproduct gives you an r that cancels out an r in the denominator. Your last equation is right.

[louf]

Why do these always begin with talking about a positive charge? I assume this is due to initial thought about charge, being "something", flows from positive to negative (sic), and the teaching continues with this practice (conventional current). To be clear, I understand electrons have a negative charge, and flow from negative to positive (electron flow).