You need a 2m long wire to carry a current of 10 mA, but you can find only a 1m

Question

You need a 2m long wire to carry a current of 10 mA, but you can find only a 1m copper wire with resistance 1 milli-ohm and a 1m wire made of some other metal. this second wire has the same length and diameter as the first wire but a resistance of 2 mili-ohms. You connect the wires in series and run the 10 mA current through them to the right. The resisitivity of copper is 1.72*10^(-8) ohm*meteres

A) what is the potential drop across the first wire

B)what is the potential drop across the second wire

C)What is the electric field in the first wire and how does it vary with position

D)What is the electric field in the second wire and how does it vary with position

E)Explain why charge builds up at the interface between the two wires, is it positive or negative

F)Estimate the surface density of charge which builds up at the intereface between the two wires

Explanation / Answer

A) V = I R = 10.0E-3*1.0E-3 = 10.0E-6 V

b) V = 10.0E-3*2.0E-3 = 20.0E-6 V

C) E = V/d 10.0E-6/1 = 10.0E-6 v/m
constant to the right

d) E = V/d = 20.0E-6/1 = 20.0E-6 V/m

e) positive charge since there is a difference in E field

f) dE = sigma/e0

sigma = e0 dE = 8.85E-12*10.0E-6 = 8.85E-17 C/m^2

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