Question

A silver wire 2.6 mm in diameter transfers a charge of 420C in 80 min. Silver contains 5.8×10²⁸ free electrons per cubic meter. What is the current in the wire? Express your answer in amperes. Part B What is the magnitude of the drift velocity of the electrons in the wire? Express your answer in meters per second.

Answer 1

The current in the silver wire is 0.0875 A. The drift velocity of the electrons in the wire is approximately 2.04 × 10^-4 m/s.

Step-by-step explanation:

To find the current in the silver wire, we can use the formula I = Q / t, where I is the current, Q is the charge transferred, and t is the time taken. Plugging in the given values, we get I = 420 C / (80 min × 60 s/min) = 0.0875 A.

To find the drift velocity of the electrons in the wire, we can use the formula I = nqAvd, where 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. We can rearrange the formula to get vd = I / (nqA). Plugging in the given values, we get vd = 0.0875 A / (5.8×1028 × 1.6×10-19 C × (π/4)(2.6 mm)2).

Calculating the drift velocity gives vd ≈ 2.04 × 10-4 m/s.