The magnetic field strength is not directly proportional to the drift velocity of electrons. Doubling the electron drift velocity does not necessarily result in an eight-fold increase in the magnetic field strength.
The magnetic field experienced by moving charges (such as electrons) can be calculated using the formula:
B = (μ₀ * I) / (2πr)
Where: B is the magnetic field strength, μ₀ is the permeability of free space, I is the current, r is the distance from the current-carrying wire.
The drift velocity of electrons is related to the current (I) in a conductor, but it is not directly proportional. The current is given by the equation:
I = n * A * v_d * q
Where: I is the current, n is the number density of charge carriers (electrons), A is the cross-sectional area of the conductor, v_d is the drift velocity of electrons, q is the charge of each electron.
From the equation, you can see that the drift velocity (v_d) is only one component of the current (I). Doubling the drift velocity will result in a doubling of the current (assuming all other factors remain constant).
However, the magnetic field strength (B) depends on the current (I) and the distance (r), as shown in the formula above. Therefore, doubling the current will only result in a doubling of the magnetic field strength if the distance (r) remains the same.
In summary, doubling the drift velocity of electrons will result in a doubling of the current, but the increase in magnetic field strength will depend on the distance from the current-carrying wire. It is not a straightforward factor of 8 increase as you mentioned.