# What causes a magnetic field to be produced at a point in space, when an electric current is flowing nearby?

We know that a current induces a magnetic field along a circular path around it But what exactly causes the magnetic field to produced in that point of space? Is it that change in the direction or magnitude of the electric field at that point in space?

If yes, can I understand the phenomenon as the magnetic field being produced due to a change in the electric field, primarily? Rather than understanding it as being produced due to current?

• A hint for experimental work. The electrons (and protons also) magnetic dipole is responsible for the magnetic field in permanent magnets. Why not explain the magnetic field of a DC current in a wire by the self induction from flowing electrons? At the start of a DC current the current was switched on and the electrons are accelerated. And the wire at the ends usually is curved, this is an acceleration too. Oct 20, 2019 at 20:29

If you look at Ampere's Law(with Maxwell's addition) you would find one term which has current density in it and one term that relates to the partial rate of change of the electric field. Depending on your system it seems to be just due to the first term which is the current which is causing the magnetic field. $$\nabla \times B = \mu_0 J +\mu_o \epsilon_0\frac{\partial E}{\partial t}$$