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A moving charge can be considered as current.
If we interpret the distance ds to be a small segment of space through which the
charge q flows. In this case the electric current is given by,
So,
, where v is the speed of the charge. Then the magnetic field is given by,
The integrand does not depend upon q and can be taken out of the integral.
Then the magnetic field will be:
Consider two parallel current carrying conductors in which an amount of current i is flowing
.
The magnitude of magnetic field at any point P will be obtained by the superposition principle:
B = B1 + B2, where B1 and B2 are given as:
The magnitude of the resultant magnetic field will be,
It can be noted that the parallel currents attract and anti-parallel currents repel.
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