We are given
diameter, d = 1.00 mm
density, ρ = 8.9 x10^3 kg/m3
magnetic field, B = 5.0 x 10^-5 T
We are asked to determine the current that would be carried by the wire
We use the formula
B = I R / A
where I is the current
R is the resistance and R = πρd / A
So,
B = I (πρd /A) / A
B = I πρd / A²
and
A is the area, A = πd²/4
So,
B = I πρd / (πd²/4)²
B = I πρd / (π² d⁴ / 16)
B = 16 I ρ / πd²
Substituting the given and solving for I
5.0 x 10^-5 = 16 I (8.9 x10^3 kg/m3) / π (1 x 10^-3)²
I = 1.1 x 10^-15 A
