If the voltage is increased then the electric field is higher, and electron velocity is proportional to this field.
What happens when the electric current through a wire increases?
As the electric current through a wire decreases, the magnetic field around the wire becomes stronger. As the electric current through a wire increases, the magnetic field around the wire becomes weaker.
How does the electric field affect current?
We also are familiar with the fact that the voltage difference between two points is also proportional to the electric field magnitude. This naturally implies that, current is proportional to the magnitude of electric field between the two points the current flows.
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