# Electric field in a wire with same current as another wire

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1. Oct 25, 2016

### ricky25j

1. The problem statement, all variables and given/known data
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?

dn = .002m
dg = .001m
Eg = .0095 N/C

ρn = 100 * 10-8 Ωm
ρg = 2.44 * 10-8 Ωm

2. Relevant equations
V = IR
R = ρL/A
V = E * Δs

3. The attempt at a solution

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).

In = Ig = Eg * Ag / ρg

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.

En = In * ρn / An
En = (Eg * Ag * ρn) / (ρg * An)

I then plugged in the values and solved.

En = [(.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?

Last edited: Oct 25, 2016
2. Oct 25, 2016

### TSny

Welcome to PF!

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