Electric field in a wire with same current as another wire

[ricky25j]

Homework Statement

For what electric field strength would the current in a 2.0-mm-diameter nichrome wire be the same as the current in a 1.0-mm-diameter gold wire in which the electric field strength is 0.0095 N/C?

d_n = .002m
d_g = .001m
E_g = .0095 N/C

ρ_n = 100 * 10^-8 Ωm
ρ_g = 2.44 * 10^-8 Ωm

Homework Equations

V = IR
R = ρL/A
V = E * Δs

The Attempt at a Solution

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First, I found a general equation for current in a wire:

V = IR
I = V/R
I = (E*Δs)/(ρL/A)
I = EA/ρ

Then, I used this to find the current in the gold wire (and by extension, the nichrome wire).

I_n = I_g = E_g * A_g / ρ_g

I then used the I = EA/ρ equation to find an expression for the electric field in the nichrome wire, and plugged in the above value for the current.

E_n = I_n * ρ_n / A_n
E_n = (E_g * A_g * ρ_n) / (ρ_g * A_n)

I then plugged in the values and solved.

E_n = [(.0095 N/C)(π*(.001m)²/4)(100*10^-8Ωm) / [(2.44*10^-8Ωm)(π*(.002m)²/4)]

= .0973 N/C

Webassign is not accepting this answer. Does anyone know where I went wrong?

 

[TSny]

Welcome to PF!

Your work looks correct. Did you get the values of the resistivities from you textbook?