A copper wire has a square cross section 2.4 mm on a side. The wire is 4.2 m lon

Question

A copper wire has a square cross section 2.4 mm on a side. The wire is 4.2 m long and carries a current of 3.7 A . The density of free electrons is 8.5×1028m3.

Part A

Find the magnitude of the current density in the wire.

Express your answer using two significant figures

Part B

Find the magnitude of the electric field in the wire.

Express your answer using two significant figures.

Part C

How much time is required for an electron to travel the length of the wire?

Express your answer using two significant figures.

Explanation / Answer

given

x = 2.4 mm = 0.0024 m

L = 4.2 m

I = 3.7 A

n = 8.5*10^28 elctrons/m^3

A)

current density, J = I/A

= I/x^2

= 3.7/0.0024^2

= 6.4*10^5 A/m^2

B) we know, resistivity of copper, rho = 1.72*10^-8 ohm.m

we know, E = rho*J

= 1.72*10^-8*6.42*10^5

= 0.011 N/c

C) drift speed, vd = J/(n*q)

= 6.42*10^5/(8.5*10^28*1.6*10^-19)

= 4.7*10^-5 m/s

time taken to travel the length of the wire,

t = L/vd

= 4.2/(4.72*10^-5)

= 8.9*10^4 s or 25 hours

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.