what must change?
the speed of the current or the direction of it?
(you mean the amount of the current)
Any change in current will do!
two wires with currents to same direction are attracted.
how a current influences a single charge?
Sorry, I don't understand your question.
The electric field must change or current must flow to create magnetism. The E field and current density are vectors so they can change either magnitude or direction.
The curl of a magnetic field is related to the time rate of change of an electric field plus any current flowing. Imagine the mag. field around a wire with AC current flowing through a capacitor. The alternating current in the wire and the changing E field in the cap. create the changing B field around the wire.
The magnetic field is really just a manifestation of the relative aspects of an changing electric field and can be explained solely with special relativity and the electric field.
The current of one wire will cause a magnetic field, which affects the charges (and current) in the other wire, and vice versa.
A moving charge q, in a magnetic field will be subject to a force F = q (v x B) where x denotes the cross product.
Alternatively, the moving charge q sees an increase in the charge of the oppositely charged ionic lattice of the other wire. Since q is moving it "sees" the wire's length contract due to SR which increases the wire's ionic lattice's charge density.
The difference in charge density creates an electric field which pulls the two wires together via F = qE. The magnitude and direction of this force is exactly the same as the Lorentz force mentioned above.
This shows that magnetism is simply an effect of changing electric fields.
Chickens and eggs. An electric field can be induced by a time changing magnetic field as well. Which comes first is a chicken and egg scenario. Which is the cause and which is the effect is an endles vicious circle.
Under ac or time-changing conditions all we can say about electric and magnetic fields is that they cannot exist independently. Neither can exist without the other, yet neither is the cause nor the effect of the other. BR.
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