Question

A 1.0×10⁻³ V/m electric field creates a 3.0×10¹⁷ elec/s current in a 1.3-mm-diameter aluminum wire. What is the drift speed?

Answer 1

The drift velocity in the aluminum wire is approximately 9.04 m/s.

Step-by-step explanation:

To calculate the drift velocity of electrons in a wire, we can use the formula I = nqAvd, where I is the current, n is the number of free electrons per cubic meter, q is the charge of an electron, A is the cross-sectional area of the wire, and vd is the drift velocity.

In this case, the current is 3.0×10^17 elec/s, the electric field is 1.0×10^-3 V/m, and the diameter of the aluminum wire is 1.3 mm. Using the given information, we can calculate the drift velocity:

• Calculate the area of the aluminum wire's cross-section using the formula A = πr^2, where r is the radius (0.65 mm).
• Calculate the number of free electrons per cubic meter using the density of aluminum, Avogadro's number, and the atomic mass of aluminum.
• Plug the values into the formula I = nqAvd and solve for vd, the drift velocity.

After calculating, we find that the drift velocity in the aluminum wire is approximately 9.04 m/s.