In a copper wire that has a diameter of 1.63 mm, the drift velocity is 7.08x10^-4 m/s. Assume that there is one free electron for conduction per copper atom. Copper has an atomic mass of 1.055x10^-25 kg and a density of about 9 g/cm^3. Required:
a. What is the current in the wire?
b. What is the current density?

(a). The current in the wire is 20.16 A.

(b). The current density is 9.66 A/mm².

Explanation:

Given that,

Diameter = 1.63 mm

Drift velocity

Atomic mass of copper

Atomic weight of copper =63.5 g

Density = 9 g/cm³  

We need to calculate the number density of electron

Using formula of number density

Where, w= atomic weight

Put the value into the formula

(a).We need to calculate the current in the wire

Using formula of drift velocity

Where, A = cross section area

q = charge of electron

n = number density of electron

= drift velocity

Put the value into the formula

(b). We need to calculate the current density

Using formula of current density

Put the value into the formula

Hence, (a). The current in the wire is 20.16 A.

(b). The current density is 9.66 A/mm².