magnetic field

[mani]

A particle of charge q, moving with a velocity vector v, is at O at a given instant. The Electrical field created by it at the point P will vary with time. This time varying Electric field sets up a magnetic field at P.
I seek confirmation that this is the same as the "usual" Magnetic field set up by a moving charge

[HallsofIvy]

And how is the "usual" magnetic field set up by a moving charge at all different from what you just said?

[mani]

In the first approach the magnetic field will be derived in terms of the time derivative of the vector electric field.
In the second approach the mag. field will be derived as q x (Vector v cross vector OP).
I am not able to prove their equality in the general case.