The resistivity of a cylindrical wire can be determined using the formula:

ρ = (R A) / L = (Rπr²)/L eq 1

The resistance R can be determined using Ohm’s law :

R=ΔV/I eq 2

The magnitude of the magnetic field at a distance y from a long straight wire is given by :

We rearrange the above expression to express the current I as

eq 3

Combining eq 1 and 2 we obtain :

eq 4

Now substituting the expression of the current (eq 3) into eq 4 we get

Given

Substituting with the given and solving for the resistivity we get

The resistivity of the wire is 1.8 × 10^-8 Ω•m

A rod has a resistance R. A craftsman fabricates the rod to create a new rod that has 4 times the length of the original rod. Assuming the new rod has the same density and resistivity, and all material is conserved, determine the rod's resistance in terms of R.